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href="//www.newsama.com/journals/amp/" aria-label="Advances in Mathematical Physics">数学物理进展</a>/<a class="sc-htpNat bUhGXt link sc-nrwXf kCVAWK breadCrumb" href="//www.newsama.com/journals/amp/contents/year/2011/" aria-label="2011">2011年</a>/<S.。pan class="sc-eitiEO cWbOKB">文章</S.。pan> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 comSpQ threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-likbZx iAOkZc section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</button> <div class="sc-bGbJRg NxRXU static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-eLExRp jWsoil sc-jtRlXQ kkipbT left_section_menu"> <p>在这一页上</p> <span class="sc-ePZHVD dxfCqj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bEjcJn JKlRH" href="#abstract" aria-label="">摘要</a></span> <span class="sc-ePZHVD dxfCqj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bEjcJn JKlRH" href="#references" aria-label="">参考文献</a></span> <span class="sc-ePZHVD dxfCqj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bEjcJn JKlRH" href="#copyright" aria-label="">版权</a></span> </div> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-hzNEM hNeCCc article_header_class"> <p class="sc-gmeYpB ctdkmR article_type">研究文章|开放获取</p> <div class="sc-kZmsYB doGfnX article_citation"> 体积 2011年 <span class="sc-iSDuPN ezntTT">|</S.。pan>文章ID. 680367 <span class="sc-iSDuPN ezntTT">|</S.。pan> <a class="sc-htpNat bUhGXt link sc-fZwumE dqIsrA" href="https://doi.org/10.1155/2011/680367" aria-label="Doi-link">https://doi.org/10.1155/2011/680367</a> </div> <div class="sc-kaNhvL kwRfSr article_full_citation"> <div class="sc-iBEsjs ezuwCV isHide"> <p>答:a . Deriglazov那 “<S.。pan class="adjust-article-svg-size">不相对论的纺丝粒子，没有基地变量和DIRAC方程</S.。pan>“，<i>数学物理进展</i>那 卷。2011年那 文章ID.680367那 10   页面那 2011年． https://doi.org/10.1155/2011/680367</p> </div> <button class="sc-hSdWYo etauus sc-LKuAh fxGnqr" color="">显示引文</button> </div> <h1 class="sc-iRbamj jZOxOO sc-RcBXQ kZecej article_title adjust-article-svg-size heading-title">不相对论的纺丝粒子，没有基地变量和DIRAC方程</h1> </div> <div class="sc-gPzReC fMlAsT article_authors"> <hr class="sc-fHxwqH kHliir hr__author"> <span class=""><b>答:a . Deriglazov</b><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-jrIrqw eeUyzW icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><sup>1</S.。up></span> <div class="sc-iQtOjA llLcVY isHide"> <p><sup>1</S.。up><span>联邦Juiz de Fora大学，36039-900 Juiz de Fora, MG，巴西</S.。pan></p> </div> <button class="sc-hSdWYo etauus sc-iybRtq clzRlh" color="">展示更多</button> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</b>斯蒂芬Anco.</div> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</S.。pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年3月31日</S.。pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">修改后的</S.。pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年7月30日</S.。pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">公认</S.。pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年8月23日</S.。pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</S.。pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年10月23日</S.。pan> </div> </div> </div> <article class="sc-jeCdPy jsyicZ article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">摘要</h4> <p>我们提出了没有格拉斯曼变量的相对论粒子模型，它通常被量子化，从而得到狄拉克方程。模型的经典动力学与狄拉克理论中相应算子的均值动力学相对应。自旋张量的经典方程与自旋粒子的Barut-Zanghi模型相同。</p> <span class="end-abs"></span> <h4 id="discussion:-nonrelativistic-spin">1.讨论:绝对的自旋</h4> <p>从古典作品开始[<a href="#B1a">1</a>-<a href="#B4b">6.</a>]，在半经典力学模型的基础上，人们花费了大量的努力来理解自旋粒子的行为[<a href="#B5">7.</a>-<a href="#B25">24</a>］．</p> <p>在给定经典理论的正则量子化过程中，我们将厄米算子与经典变量联系起来。让<S.。vg height="11.425" id="M1" style="vertical-align:-0.17555pt;width:14.7125px;" version="1.1" viewbox="0 0 14.7125 11.425" width="14.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.425)"> <g transform="translate(72,-62.86)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-37.44,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.S.pan> </text> </g> </g> </svg>是对应的经典方括号。(不带二次约束理论中的泊松(狄拉克)方括号)根据狄拉克量子化范式[<a href="#B2">3.</a>]，运营商<S.。vg height="11.6" id="M3" style="vertical-align:-0.17555pt;width:14.7125px;" version="1.1" viewbox="0 0 14.7125 11.6" width="14.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.6)"> <g transform="translate(72,-62.72)"> <text transform="matrix(1,0,0,-1,-65.32,62.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.6265898" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.71,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>必须选择服从量化规则吗<S.。pan class="equation" id="EEq1"> <svg height="20.3375" id="M4" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.3375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.3375)"> <g transform="translate(72,-55.73)"> <text transform="matrix(1,0,0,-1,134.78,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="11.41" y="-2.51"> ̂</T.S.pan> <tspan style="font-size: 12.50px; " x="4.7959132" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,145.8,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,151.24,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="11.827838" y="0"> ̂</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,162.69,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,168.07,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="43.27" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="50.459999" y="-2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.8699999" y="-2.51"> ∓</T.S.pan> <tspan style="font-size: 12.50px; " x="18.897886" y="-2.51"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="30.938274" y="-2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="34.82671" y="-2.51"> ℏ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,224.77,65.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,230.2,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,241.65,65.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,247.03,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.1900001" y="-4.1300001"> |</T.S.pan> <tspan style="font-size: 12.50px; " x="7.1900001" y="-0.89999998"> |</T.S.pan> </text> <text transform="matrix(1,0,0,-1,256.72,55.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.8288321" y="0"> →</T.S.pan> </text> <text transform="matrix(1,0,0,-1,278.74,55.96)"> <tspan style="font-size: 12.50px; " x="0.11" y="-5"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.6265898" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="186.00999" y="-4.7800002"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="190.17349" y="-4.7800002"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="196.425" y="-4.7800002"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="199.55075" y="-4.7800002"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="205.80225" y="-4.7800002"> ）</T.S.pan> </text> </g> </g> </svg></span>在该等方程中，我们采用换向器（抗制者）的反对二手（对称）经典支架。在偶数（奇数= Grassmann）变量的经典机制中出现反对称（对称）经典支架。</p> <p>自旋量子理论是已知的(它是由非相对论的泡利(狄拉克)方程(相对论)情况下),搜索相应的半经典模型代表了逆正则量子化的任务:我们寻找经典力学系统的古典托架遵循(<a href="#EEq1">1．1</a>）对于已知的左侧。非旋转旋转操作员的组件<S.。vg height="19.549999" id="M5" style="vertical-align:-3.2316pt;width:79.612503px;" version="1.1" viewbox="0 0 79.612503 19.549999" width="79.612503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.55)"> <g transform="translate(72,-56.36)"> <text transform="matrix(1,0,0,-1,-70.95,62.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-1" y="2.73"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,56.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.25,59.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="23.430622" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="33.157955" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="37.321453" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-11.58,64.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>（<S.。vg height="13.2875" id="M6" style="vertical-align:-0.13794pt;width:13.325px;" version="1.1" viewbox="0 0 13.325 13.2875" width="13.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.2875)"> <g transform="translate(72,-61.37)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>是保利矩阵（<a href="#EEq5">1．5</a>））相对于换向器形成一个简单的代数<S.。pan class="equation" id="EEq2"> <svg height="29.512501" id="M7" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 29.512501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,29.5125)"> <g transform="translate(72,-48.39)"> <text transform="matrix(1,0,0,-1,153.33,52.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.7399998" y="-7.6500001"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.7399998" y="-4.9200001"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,168.07,54.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,171.29,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="6.21" y="-2.73"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.21" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,185.51,54.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,189.93,52.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,195.67,48.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.S.pan> </text> <text transform="matrix(1,0,0,-1,205.64,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.916319" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="23.155556" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,234.68,54.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.1264" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,247.05,60.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-1" y="2.73"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,255.05,54.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,260.29,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="204.46001" y="0.22"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="208.6235" y="0.22"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="214.875" y="0.22"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="218.00075" y="0.22"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="224.25224" y="0.22"> ）</T.S.pan> </text> </g> </g> </svg></span>以及反交换子<S.。pan class="equation" id="EEq3"> <svg height="34.662498" id="M8" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 34.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,34.6625)"> <g transform="translate(72,-44.27)"> <text transform="matrix(1,0,0,-1,160.67,48.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.7399998" y="-7.6500001"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.7399998" y="-4.9200001"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,175.41,50.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,178.63,53.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="6.21" y="-2.73"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.21" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,192.84,50.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,197.27,48.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,203.01,44.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</T.S.pan> </text> <text transform="matrix(1,0,0,-1,212.98,53.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="13.23" y="-7.2600002"> ℏ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,233.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <g> <path d="m 226.21,56.65 12.11,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,229.14,44.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="10.38" y="-8.75"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,245.81,50.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,252.96,53.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="211.78999" y="-1.49"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="215.95351" y="-1.49"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="222.205" y="-1.49"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="225.33075" y="-1.49"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="231.58224" y="-1.49"> ）</T.S.pan> </text> </g> </g> </svg></span>因此，算子可以从基于偶或奇自旋空间变量的经典模型开始产生。</p> <p>在他们的先锋工作中[<a href="#B11a">13</a>那<a href="#B11b">14</a>]， Berezin和Marinov建立了基于奇变量的模型，并表明它为非相对论和相对论自旋的半经典描述提供了非常经济的方案。他们的处方可以很快恢复如下。对于非相对论自旋，非相互作用的拉格朗日量是<S.。vg height="18.012501" id="M9" style="vertical-align:-3.2316pt;width:131.1375px;" version="1.1" viewbox="0 0 131.1375 18.012501" width="131.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.0125)"> <g transform="translate(72,-57.59)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="13.040629" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="16.516462" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="22.767963" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="26.931461" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="37.396473" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="31.094961" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-33.98,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-30.76,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-26.59,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-18.94,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="15.50372" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="22.867987" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="29.119488" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="33.282986" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,20.38,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,29.5,63.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-5.9000001" y="2.73"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,29.64,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>，其中自旋内部空间是由类矢量格拉斯曼变量构造的<S.。vg height="14.5875" id="M10" style="vertical-align:-3.2316pt;width:11.7px;" version="1.1" viewbox="0 0 11.7 14.5875" width="11.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.91,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="16.512501" id="M11" style="vertical-align:-4.77652pt;width:79.537498px;" version="1.1" viewbox="0 0 79.537498 16.512501" width="79.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.91,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.69,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.65,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-48.75,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-22.11,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-17.68,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-11.64,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．自拉格朗日是线性的<S.。vg height="17.275" id="M12" style="vertical-align:-3.2316pt;width:11.7px;" version="1.1" viewbox="0 0 11.7 17.275" width="11.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.275)"> <g transform="translate(72,-58.18)"> <text transform="matrix(1,0,0,-1,-66.05,64.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-5.9000001" y="2.72"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.91,58.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>，它们的共轭动量与<S.。vg height="13.425" id="M13" style="vertical-align:-2.29482pt;width:7.6750002px;" version="1.1" viewbox="0 0 7.6750002 13.425" width="7.6750002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="17.275" id="M14" style="vertical-align:-3.2316pt;width:111.825px;" version="1.1" viewbox="0 0 111.825 17.275" width="111.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.275)"> <g transform="translate(72,-58.18)"> <text transform="matrix(1,0,0,-1,-71.95,61.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,58.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.66,61.45)"> <tspan style="font-size: 12.50px; " x="43.040001" y="-2.72"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="37.150002" y="-7.1054274e-015"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="18.429422" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="27.281546" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="30.75738" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-14.47,58.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-7.78,61.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.916319" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,14.19,58.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．这些关系代表狄拉克的二级约束，并通过从奇泊松方括号到狄拉克方括号的转换来考虑<S.。pan class="equation" id="EEq4"> <svg height="20.137501" id="M15" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.137501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.1375)"> <g transform="translate(72,-55.89)"> <text transform="matrix(1,0,0,-1,164.41,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.1900001" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,177.64,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,180.86,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,192.11,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,196.53,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,203.72,55.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> D.</T.S.pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> B.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,219.85,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.916319" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,242.07,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,249.22,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="215.53" y="0.31"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="219.6935" y="0.31"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="225.94499" y="0.31"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="229.07076" y="0.31"> 4.</T.S.pan> <tspan style="font-size: 12.50px; " x="235.32225" y="0.31"> ）</T.S.pan> </text> </g> </g> </svg></span>处理狄拉克托架，可以解决约束，排除动量的考虑。所以只有三个自旋变量<S.。vg height="14.5875" id="M16" style="vertical-align:-3.2316pt;width:11.7px;" version="1.1" viewbox="0 0 11.7 14.5875" width="11.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.91,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>用所需的括号(<a href="#EEq4">1．4</a>）.根据(<a href="#EEq1">1．1</a>），（<a href="#EEq4">1．4</a>），和（<a href="#EEq3">1．3</a>），通过旋转操作员替换变量来执行规范量化<S.。vg height="19.549999" id="M17" style="vertical-align:-3.2316pt;width:15.4px;" version="1.1" viewbox="0 0 15.4 19.549999" width="15.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.55)"> <g transform="translate(72,-56.36)"> <text transform="matrix(1,0,0,-1,-70.95,62.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-1" y="2.73"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,56.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>与pauli成比例<S.。vg height="6.9875002" id="M18" style="vertical-align:-0.13794pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>矩阵,<S.。vg height="19.549999" id="M19" style="vertical-align:-3.2316pt;width:79.612503px;" version="1.1" viewbox="0 0 79.612503 19.549999" width="79.612503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.55)"> <g transform="translate(72,-56.36)"> <text transform="matrix(1,0,0,-1,-70.95,62.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-1" y="2.73"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,56.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.25,59.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="23.430622" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="33.157955" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="37.321453" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-11.58,64.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="17.5625" id="M20" style="vertical-align:-3.49493pt;width:97.074997px;" version="1.1" viewbox="0 0 97.074997 17.5625" width="97.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.5625)"> <g transform="translate(72,-57.95)"> <text transform="matrix(1,0,0,-1,-71.95,61.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> [</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-60.45,66.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.23,61.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-44.68,66.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-40.25,61.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-36.09,58.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-26.12,61.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-1.54,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。pan class="equation" id="EEq5"> <svg height="62.637501" id="M21" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 62.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,62.6375)"> <g transform="translate(72,-21.89)"> <text transform="matrix(1,0,0,-1,84.98,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,92.32,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</T.S.pan> </text> <text transform="matrix(1,0,0,-1,100.67,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.08"> ⎛</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.23"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.6099997"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="19.4"> ⎝</T.S.pan> <tspan style="font-size: 12.50px; " x="36.139999" y="-13.08"> ⎞</T.S.pan> <tspan style="font-size: 12.50px; " x="36.139999" y="-2.23"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="36.139999" y="8.6099997"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="36.139999" y="19.4"> ⎠</T.S.pan> <tspan style="font-size: 12.50px; " x="17.66" y="-10.63"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="29.887934" y="-10.63"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="17.66" y="14.38"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="29.887934" y="14.38"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="43.849998" y="7.1054274e-015"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="68.981033" y="7.1054274e-015"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,177,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,185.35,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.03" y="-13.08"> ⎛</T.S.pan> <tspan style="font-size: 12.50px; " x="12.03" y="-2.23"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.03" y="8.6099997"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.03" y="19.4"> ⎝</T.S.pan> <tspan style="font-size: 12.50px; " x="42.34" y="-13.08"> ⎞</T.S.pan> <tspan style="font-size: 12.50px; " x="42.34" y="-2.23"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="42.34" y="8.6099997"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="42.34" y="19.4"> ⎠</T.S.pan> <tspan style="font-size: 12.50px; " x="17.66" y="-10.63"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="29.887934" y="-10.63"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="38.452488" y="-10.63"> </T.S.pan> <tspan style="font-size: 12.50px; " x="18.84" y="14.38"> </T.S.pan> <tspan style="font-size: 12.50px; " x="32.980892" y="14.38"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="50.049999" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="75.18103" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,267.88,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,276.22,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.08"> ⎛</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.23"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.6099997"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="19.4"> ⎝</T.S.pan> <tspan style="font-size: 12.50px; " x="44.709999" y="-13.08"> ⎞</T.S.pan> <tspan style="font-size: 12.50px; " x="44.709999" y="-2.23"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="44.709999" y="8.6099997"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="44.709999" y="19.4"> ⎠</T.S.pan> <tspan style="font-size: 12.50px; " x="17.67" y="-10.63"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="34.173962" y="-10.63"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="17.67" y="14.38"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="29.885431" y="14.38"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="38.449986" y="14.38"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="52.419998" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="188.53" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="192.6935" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="198.94499" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="202.07076" y="0"> 5.</T.S.pan> <tspan style="font-size: 12.50px; " x="208.32225" y="0"> ）</T.S.pan> </text> </g> </g> </svg></span>采取二维旋转空间<S.。vg height="16.025" id="M22" style="vertical-align:-3.22282pt;width:48.987499px;" version="1.1" viewbox="0 0 48.987499 16.025" width="48.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.025)"> <g transform="translate(72,-59.18)"> <text transform="matrix(1,0,0,-1,-71.95,62.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.62,59.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.19,62.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> ⃗</T.S.pan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="20.167339" y="0"> ）</T.S.pan> </text> </g> </g> </svg>．外部电磁背景上的粒子的规范量化导致Pauli方程<S.。pan class="equation" id="EEq6"> <svg height="38.575001" id="M23" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,82.02,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="3.888433" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="12.33" y="-7.25"> </T.S.pan> <tspan style="font-size: 12.50px; " x="18.70653" y="-7.25"> Ψ</T.S.pan> </text> <g> <path d="m 94.35,56.57 15.71,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,97.05,44.69)"> <tspan style="font-size: 12.50px; " x="17.68" y="-8.7600002"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="29.719999" y="-1.4299999"> </T.S.pan> <tspan style="font-size: 12.50px; " x="44.73" y="-16.01"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </T.S.pan> </text> <g> <path d="m 137.34,56.57 15.13,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,137.34,44.69)"> <tspan style="font-size: 12.50px; " x="16.33" y="-3.8399999"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="30.57" y="-8.7600002"> ̂</T.S.pan> <tspan style="font-size: 12.50px; " x="23.69335" y="-8.7600002"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,167.14,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,173.14,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="12.67" y="-7.25"> </T.S.pan> </text> <g> <path d="m 185.68,56.57 5.82,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,185.68,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.0100002" y="-8.7600002"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,201.66,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,204.88,48.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,212.48,64.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,220.13,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="16.904057" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,246,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,253.66,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="16.6" y="-7.25"> </T.S.pan> <tspan style="font-size: 12.50px; " x="22.163836" y="-7.25"> ℏ</T.S.pan> </text> <g> <path d="m 266.19,56.57 20.95,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,266.19,44.69)"> <tspan style="font-size: 12.50px; " x="22.139999" y="-8.7600002"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.12863" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,297.03,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,300.25,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,307.59,58.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,310.81,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="11.46" y="-7.3299999"> Ψ</T.S.pan> <tspan style="font-size: 12.50px; " x="20.787237" y="-7.3299999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="153.94" y="-7.3299999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="158.1035" y="-7.3299999"> 1</T.S.pan> <tspan style="font-size: 12.50px; 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" x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</T.S.pan> </text> </g> </g> </svg>．以类似的方式描述相对论的旋转[<a href="#B11a">13</a>那<a href="#B11b">14</a>］．</p> <p>这里的问题是，格拉斯曼经典力学代表了一个相当正式的数学结构。这会导致某些困难[<a href="#B11a">13</a>那<a href="#B11b">14</a>那<a href="#B14">17</a>]试图用它来描述在量子化之前的半经典能级上的自旋效应。因此，在常用变量的基础上描述自旋是很有趣的。这个问题由来已久(参见[<a href="#B5">7.</a>-<a href="#B12">15</a>)，到目前为止似乎没有完全令人满意的解决方案。这似乎出奇地难[<a href="#B12">15</a>]以一种系统的方式，构建一个一致的模型，从而在正则量子化过程中产生狄拉克方程。本文的目的是建立狄拉克方程的力学模型的一个例子。</p> <p>用交换变量描述非相对论自旋，我们需要建立一个包含交换子(偶)算子代数的力学模型(<a href="#EEq2">1．2</a>)而不是反交换子(<a href="#EEq3">1．3</a>）.这在最近的工作中已经实现了。<a href="#B15">18</a>]从拉格朗日开始<S.。pan class="equation" id="EEq7"> <svg height="38.400002" id="M29" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.400002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.4)"> <g transform="translate(72,-41.28)"> <text transform="matrix(1,0,0,-1,-0.98,52.42)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="11.34" y="-3.8299999"> </T.S.pan> <tspan style="font-size: 12.50px; " x="18.709999" y="-6.2399998"> </T.S.pan> <tspan style="font-size: 12.50px; " x="24.559999" y="-8.75"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,365.7,49.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,368.92,49.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,374.77,59.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,382.43,52.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,400.05,57.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,404.92,47.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="9.6899996" y="-4.9200001"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="59.830002" y="-6.02"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="63.9935" y="-6.02"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="70.245003" y="-6.02"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="73.37075" y="-6.02"> 7.</T.S.pan> <tspan style="font-size: 12.50px; " x="79.622246" y="-6.02"> ）</T.S.pan> </text> </g> </g> </svg></span>配置空间变量是<S.。vg height="14.7125" id="M30" style="vertical-align:-3.2316pt;width:28.049999px;" version="1.1" viewbox="0 0 28.049999 14.7125" width="28.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-61.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.7125" id="M31" style="vertical-align:-3.2316pt;width:30.0875px;" version="1.1" viewbox="0 0 30.0875 14.7125" width="30.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-60.22,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.6125" id="M32" style="vertical-align:-2.34499pt;width:23.112499px;" version="1.1" viewbox="0 0 23.112499 13.6125" width="23.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.1514759" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="10.314975" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="14.228414" y="0"> ）</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.55" id="M33" style="vertical-align:-2.29482pt;width:25.5px;" version="1.1" viewbox="0 0 25.5 13.55" width="25.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.064435" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="12.227934" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="16.141373" y="0"> ）</T.S.pan> </text> </g> </g> </svg>．这里<S.。vg height="11.05" id="M34" style="vertical-align:-3.2316pt;width:12.75px;" version="1.1" viewbox="0 0 12.75 11.05" width="12.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>表示质点与质量的空间坐标<S.。vg height="7.1374998" id="M35" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>和费用<S.。vg height="7.1875" id="M36" style="vertical-align:-0.13794pt;width:7.0749998px;" version="1.1" viewbox="0 0 7.0749998 7.1875" width="7.0749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="11.05" id="M37" style="vertical-align:-3.2316pt;width:14.7875px;" version="1.1" viewbox="0 0 14.7875 11.05" width="14.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>是旋转空间坐标，<S.。vg height="9.9375" id="M38" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.425" id="M39" style="vertical-align:-2.29482pt;width:10.2px;" version="1.1" viewbox="0 0 10.2 13.425" width="10.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>辅助变量和<S.。vg height="9.3249998" id="M40" style="vertical-align:-0.1254pt;width:60.224998px;" version="1.1" viewbox="0 0 60.224998 9.3249998" width="60.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.325)"> <g transform="translate(72,-64.54)"> <text transform="matrix(1,0,0,-1,-71.95,64.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> C</T.S.pan> <tspan style="font-size: 12.50px; " x="27.331558" y="0"> O.</T.S.pan> <tspan style="font-size: 12.50px; " x="33.583057" y="0"> N</T.S.pan> <tspan style="font-size: 12.50px; " x="39.834557" y="0"> S.</T.S.pan> <tspan style="font-size: 12.50px; " x="44.610703" y="0"> T.</T.S.pan> </text> </g> </g> </svg>．第二及第三届任期(<a href="#EEq7">1．7</a>)表示与向量势的最小相互作用<S.。vg height="14.6125" id="M41" style="vertical-align:-3.25793pt;width:17.424999px;" version="1.1" viewbox="0 0 17.424999 14.6125" width="17.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6125)"> <g transform="translate(72,-60.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.575" id="M42" style="vertical-align:-3.2316pt;width:15.35px;" version="1.1" viewbox="0 0 15.35 14.575" width="15.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.575)"> <g transform="translate(72,-60.34)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>而第四项包含自旋与磁场的相互作用。最后，它产生了量子力学哈密顿量中的泡利项。</p> <p>模型中的Dirac约束暗示[<a href="#B15">18</a>]旋转终身在六维旋转相空间的二维表面上<S.。vg height="11.05" id="M43" style="vertical-align:-3.2316pt;width:14.7875px;" version="1.1" viewbox="0 0 14.7875 11.05" width="14.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="10.8375" id="M44" style="vertical-align:-3.2316pt;width:13.65px;" version="1.1" viewbox="0 0 13.65 10.8375" width="13.65" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8375)"> <g transform="translate(72,-63.33)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．曲面可以用角动量坐标参数化<S.。vg height="16.512501" id="M45" style="vertical-align:-4.77652pt;width:87.487503px;" version="1.1" viewbox="0 0 87.487503 16.512501" width="87.487503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.13,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-39.22,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.1264" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-27.85,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-19.33,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-14.91,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-7.3,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>，受到条件<S.。vg height="14.3125" id="M46" style="vertical-align:-0.17555pt;width:71.974998px;" version="1.1" viewbox="0 0 71.974998 14.3125" width="71.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3125)"> <g transform="translate(72,-60.55)"> <text transform="matrix(1,0,0,-1,-71.95,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,65.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-54.6,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> ℏ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-29.07,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-24.2,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 4.</T.S.pan> </text> </g> </g> </svg>．他们服从经典的托架<S.。vg height="16.700001" id="M47" style="vertical-align:-4.77652pt;width:109.175px;" version="1.1" viewbox="0 0 109.175 16.700001" width="109.175" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7)"> <g transform="translate(72,-58.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</T.S.pan> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.82,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-54.6,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-41.26,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-36.84,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.S.pan> <tspan style="font-size: 12.50px; " x="9.4772739" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="21.505159" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-9.45,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.1264" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,1.92,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,10.05,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．因此我们根据这个规则将它们量子化<S.。vg height="19.549999" id="M48" style="vertical-align:-3.2316pt;width:57.950001px;" version="1.1" viewbox="0 0 57.950001 19.549999" width="57.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.55)"> <g transform="translate(72,-56.36)"> <text transform="matrix(1,0,0,-1,-71.95,59.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.82,56.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.05,59.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> →</T.S.pan> <tspan style="font-size: 12.50px; " x="18.139999" y="-2.73"> </T.S.pan> <tspan style="font-size: 12.50px; " x="17.139999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-28.91,56.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．</p> <p>该模型在经典能级和量子能级上都得到了合理的描述。经典动力学是由拉格朗日方程控制的<S.。pan class="equation" id="EEq8"> <svg height="65.474998" id="M49" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 65.474998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,65.475)"> <g transform="translate(72,-19.62)"> <text transform="matrix(1,0,0,-1,115.28,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.191145" y="0"> ̈</T.S.pan> <tspan style="font-size: 12.50px; " x="8.8896332" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,131.04,56.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,137.73,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,164.26,56.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,170.26,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="12.66" y="-7.2600002"> </T.S.pan> </text> <g> <path d="m 182.8,62.31 5.81,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,182.8,50.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.0100002" y="-8.75"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,195.68,56.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.1264" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,213.37,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.3140149" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,213.93,56.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,218.36,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,227.06,56.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,235.08,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="17.1" y="-7.2600002"> </T.S.pan> </text> <g> <path d="m 247.62,62.31 14.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,247.62,50.43)"> <tspan style="font-size: 12.50px; " x="15.88" y="-8.75"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.8771296" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,271.63,56.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,276.87,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,283.26,56.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,286.48,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,295.18,56.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,300.43,59.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="-129.03999" y="27.889999"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-136.42" y="30.620001"> </T.S.pan> <tspan style="font-size: 12.50px; " x="164.32001" y="1.1799999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="168.48351" y="1.1799999"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="174.735" y="1.1799999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="177.86075" y="1.1799999"> 8.</T.S.pan> <tspan style="font-size: 12.50px; " x="184.11224" y="1.1799999"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,172.14,25.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,178.83,28.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="17.799999" y="-7.25"> </T.S.pan> </text> <g> <path d="m 192.07,31.69 14.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,192.07,19.81)"> <tspan style="font-size: 12.50px; " x="15.88" y="-8.75"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.8771296" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,213.83,25.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.1264" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,225.2,28.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,233.32,25.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,237.75,28.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,246.45,25.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,251.7,28.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="213.05" y="1.1900001"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="217.2135" y="1.1900001"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="223.465" y="1.1900001"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="226.59074" y="1.1900001"> 9.</T.S.pan> <tspan style="font-size: 12.50px; " x="232.84225" y="1.1900001"> ）</T.S.pan> </text> </g> </g> </svg></span>它已经表示<S.。vg height="14.75" id="M51" style="vertical-align:-3.25793pt;width:163.6375px;" version="1.1" viewbox="0 0 163.6375 14.75" width="163.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.390473" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="24.430862" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="32.995419" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="43.410416" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="46.88625" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="52.074993" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="56.238495" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="60.401993" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="66.791023" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="75.755676" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="79.231514" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="85.620544" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="89.533981" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="96.473145" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="107.82587" y="0"> ∇</T.S.pan> <tspan style="font-size: 12.50px; " x="116.96557" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,53.98,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>．自从<S.。vg height="14.25" id="M52" style="vertical-align:-0.1254pt;width:52px;" version="1.1" viewbox="0 0 52 14.25" width="52" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.25)"> <g transform="translate(72,-60.6)"> <text transform="matrix(1,0,0,-1,-71.95,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,65.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-54.6,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≈</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> ℏ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-35.32,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> </g> </g> </svg>，这<S.。vg height="10.725" id="M53" style="vertical-align:-0.1254pt;width:11.375px;" version="1.1" viewbox="0 0 11.375 10.725" width="11.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>-term从(中消失<a href="#EEq8">1．8</a>）在古典的极限中<S.。vg height="11.0125" id="M54" style="vertical-align:-0.17555pt;width:45.349998px;" version="1.1" viewbox="0 0 45.349998 11.0125" width="45.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="12.790569" y="0"> →</T.S.pan> <tspan style="font-size: 12.50px; " x="29.91968" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>．然后(<a href="#EEq8">1．8</a>)在外部电磁场中再现经典运动。还要注意的是，在没有相互作用的情况下，旋转的粒子不会遇到不希望的情况<i>zitterbewung</i>．方程(<a href="#EEq8">1．9</a>)描述了外磁场中的经典自旋进动。另一方面，模型的正则量子化立即产生泡利方程(<a href="#EEq6">1．6</a>）.</p> <p>下面，我们将该方案概括为相对论的情况，将角动量变量作为旋转空间的基本坐标。在这个基础上，我们构造了在规范量化之后产生DIRAC方程的相对论不变的经典力学，并简要讨论其经典动态。</p> <h4 id="algebraic-construction-of-the-relativistic-spin-space">2.相对论自旋空间的代数构造</h4> <p>我们从相对论自旋空间的模型独立构造开始。可以得到包含三维自旋矢量的自旋进动的相对论性方程<S.。vg height="18.3125" id="M55" style="vertical-align:-0.17555pt;width:15.4px;" version="1.1" viewbox="0 0 15.4 18.3125" width="15.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.3125)"> <g transform="translate(72,-57.35)"> <text transform="matrix(1,0,0,-1,-70.95,60.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; 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" x="0" y="0"> Φ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.41,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-52.19,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-46.26,59.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-37.9,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>，或进入巴格曼-米歇尔-特勒格迪四矢量(条件<S.。vg height="15.2625" id="M58" style="vertical-align:-3.21404pt;width:65.550003px;" version="1.1" viewbox="0 0 65.550003 15.2625" width="65.550003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.2625)"> <g transform="translate(72,-59.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; 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" x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.12,63.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-51.19,60.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-41.89,63.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>保证在剩余帧中只能在这些数量的三个部件中生存，这意味着正确的非椭圆性极限）。<S.。vg height="11.3" id="M60" style="vertical-align:-0.1254pt;width:18.6625px;" version="1.1" viewbox="0 0 18.6625 11.3" width="18.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3)"> <g transform="translate(72,-62.96)"> <text transform="matrix(1,0,0,-1,-71.95,63.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="17.049999" id="M61" style="vertical-align:-4.74141pt;width:60.5625px;" version="1.1" viewbox="0 0 60.5625 17.049999" width="60.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.05)"> <g transform="translate(72,-58.36)"> <text transform="matrix(1,0,0,-1,-71.95,63.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.12,63.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-51.19,60.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-41.89,63.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>,在那里<S.。vg height="12.925" id="M62" style="vertical-align:-4.74141pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 12.925" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-66.02,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>表示粒子的四速度。不幸的是，基于这些方案的半经典模型不能产生合理的量子理论，因为它们不能通过正则量子化产生狄拉克方程。我们现在的动机是，它可以在意味着包括的提法中实现<S.。vg height="19.549999" id="M63" style="vertical-align:-3.2316pt;width:15.4px;" version="1.1" viewbox="0 0 15.4 19.549999" width="15.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.55)"> <g transform="translate(72,-56.36)"> <text transform="matrix(1,0,0,-1,-70.95,62.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-1" y="2.73"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,56.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>进入<S.。vg height="13.45" id="M64" style="vertical-align:-2.21957pt;width:54.275002px;" version="1.1" viewbox="0 0 54.275002 13.45" width="54.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.1269503" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="17.279146" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="21.442644" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="32.895393" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="39.146893" y="0"> ）</T.S.pan> </text> </g> </g> </svg>角动量张量<S.。vg height="18.475" id="M65" style="vertical-align:-0.17555pt;width:27.7125px;" version="1.1" viewbox="0 0 27.7125 18.475" width="27.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.475)"> <g transform="translate(72,-57.22)"> <text transform="matrix(1,0,0,-1,-71.04,59.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.91000003" y="2.53"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.1,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> </g> </g> </svg>五维闵可夫斯基空间<S.。vg height="13.7375" id="M66" style="vertical-align:-2.29482pt;width:223.2px;" version="1.1" viewbox="0 0 223.2 13.7375" width="223.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7375)"> <g transform="translate(72,-61.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.427982" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="24.46837" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="28.63187" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="36.246197" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="41.459949" y="0"> 5.</T.S.pan> <tspan style="font-size: 12.50px; " x="47.711449" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="55.33828" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; 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" x="156.57507" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="162.82657" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="168.04031" y="0"> 5.</T.S.pan> <tspan style="font-size: 12.50px; " x="174.29182" y="0"> ）</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="16.5375" id="M67" style="vertical-align:-2.29482pt;width:121.675px;" version="1.1" viewbox="0 0 121.675 16.5375" width="121.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.7,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-49.01,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; 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" x="0" y="0"> ̂</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.8766499" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.84,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.53,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="24.480873" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="31.720112" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-18.42,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．我们用厄米矩阵表示<S.。vg height="13.775" id="M70" style="vertical-align:-0.0pt;width:15.3875px;" version="1.1" viewbox="0 0 15.3875 13.775" width="15.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.775)"> <g transform="translate(72,-60.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>和anti-Hermitian<S.。vg height="13.1125" id="M71" style="vertical-align:-0.0pt;width:13.325px;" version="1.1" viewbox="0 0 13.325 13.1125" width="13.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.1125)"> <g transform="translate(72,-61.51)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg><span class="equation" id="EEq11"> <svg height="62.637501" id="M72" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 62.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,62.6375)"> <g transform="translate(72,-21.89)"> <text transform="matrix(1,0,0,-1,122.66,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,130,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,138.34,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.08"> ⎛</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.23"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.6099997"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="19.4"> ⎝</T.S.pan> <tspan style="font-size: 12.50px; " x="44.709999" y="-13.08"> ⎞</T.S.pan> <tspan style="font-size: 12.50px; " x="44.709999" y="-2.23"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="44.709999" y="8.6099997"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="44.709999" y="19.4"> ⎠</T.S.pan> <tspan style="font-size: 12.50px; " x="17.67" y="-10.63"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="34.173962" y="-10.63"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="17.67" y="14.38"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="29.897934" y="14.38"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="38.46249" y="14.38"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="52.419998" y="7.1054274e-015"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="77.551033" y="7.1054274e-015"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,223.24,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,229.93,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.08"> ⎛</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.23"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.6099997"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="19.4"> ⎝</T.S.pan> <tspan style="font-size: 12.50px; " x="24.1" y="-10.63"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="42.766979" y="-10.63"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,280.04,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,247.6,29.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,263.5,34.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,274.85,29.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="-27.459999"> ⎞</T.S.pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="-16.610001"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="-5.77"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="5.02"> ⎠</T.S.pan> <tspan style="font-size: 12.50px; " x="16.120001" y="-14.38"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="189.89999" y="-14.38"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="194.06349" y="-14.38"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="200.315" y="-14.38"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="203.44075" y="-14.38"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="209.69225" y="-14.38"> ）</T.S.pan> </text> </g> </g> </svg></span>然后<S.。vg height="15.6125" id="M73" style="vertical-align:-3.49493pt;width:115.4125px;" version="1.1" viewbox="0 0 115.4125 15.6125" width="115.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6125)"> <g transform="translate(72,-59.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> [</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-60.45,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-54.62,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-42.07,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-37.18,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-33.01,59.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-23.05,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,10.06,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.1125" id="M74" style="vertical-align:-2.29482pt;width:100.2875px;" version="1.1" viewbox="0 0 100.2875 14.1125" width="100.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1125)"> <g transform="translate(72,-60.71)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.7,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-52,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="27.531607" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="38.871826" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="47.436382" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="56.000938" y="0"> ）</T.S.pan> </text> </g> </g> </svg>,<S.。vg height="13.775" id="M75" style="vertical-align:-0.0pt;width:28.5875px;" version="1.1" viewbox="0 0 28.5875 13.775" width="28.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.775)"> <g transform="translate(72,-60.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-59.74,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-52.4,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.775" id="M76" style="vertical-align:-0.0pt;width:15.3875px;" version="1.1" viewbox="0 0 15.3875 13.775" width="15.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.775)"> <g transform="translate(72,-60.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>DIRAC矩阵[<a href="#B2">3.</a>]<S.。vg height="13.275" id="M77" style="vertical-align:-0.1254pt;width:12.9625px;" version="1.1" viewbox="0 0 12.9625 13.275" width="12.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.275)"> <g transform="translate(72,-61.38)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.9,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.425" id="M78" style="vertical-align:-2.29482pt;width:8.8500004px;" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg><span class="equation" id="EEq12"> <svg height="62.637501" id="M79" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 62.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,62.6375)"> <g transform="translate(72,-21.89)"> <text transform="matrix(1,0,0,-1,129.7,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,136.75,48.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,143.45,43.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-13.08"> ⎛</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="-2.23"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="8.6099997"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="19.4"> ⎝</T.S.pan> <tspan style="font-size: 12.50px; " x="19.82" y="-10.63"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="34.198448" y="-10.63"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,184.99,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,161.11,29.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,168.45,34.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,179.8,29.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="-27.459999"> ⎞</T.S.pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="-16.610001"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="-5.77"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="8.4099998" y="5.02"> ⎠</T.S.pan> <tspan style="font-size: 12.50px; " x="63.740002" y="-27.459999"> ⎛</T.S.pan> <tspan style="font-size: 12.50px; " x="63.740002" y="-16.610001"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="63.740002" y="-5.77"> ⎜</T.S.pan> <tspan style="font-size: 12.50px; " x="63.740002" y="5.02"> ⎝</T.S.pan> <tspan style="font-size: 12.50px; " x="96.410004" y="-27.459999"> ⎞</T.S.pan> <tspan style="font-size: 12.50px; " x="96.410004" y="-16.610001"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="96.410004" y="-5.77"> ⎟</T.S.pan> <tspan style="font-size: 12.50px; " x="96.410004" y="5.02"> ⎠</T.S.pan> <tspan style="font-size: 12.50px; " x="16.120001" y="-14.38"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="41.25103" y="-14.38"> </T.S.pan> <tspan style="font-size: 12.50px; " x="51.691036" y="-14.38"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="69.370003" y="-25.01"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="85.873962" y="-25.01"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="69.370003" y="3.5527137e-015"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="81.585434" y="3.5527137e-015"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="90.149986" y="3.5527137e-015"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="104.12" y="-14.38"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="284.95001" y="-14.38"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="289.11349" y="-14.38"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="295.36499" y="-14.38"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="298.49075" y="-14.38"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="304.74225" y="-14.38"> ）</T.S.pan> </text> </g> </g> </svg></span>我们取算子的经典对应项<S.。vg height="11.375" id="M80" style="vertical-align:-0.17555pt;width:16px;" version="1.1" viewbox="0 0 16 11.375" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.375)"> <g transform="translate(72,-62.9)"> <text transform="matrix(1,0,0,-1,-65.27,63.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.6766019" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>和<S.。vg height="16.7125" id="M81" style="vertical-align:-4.74141pt;width:74.324997px;" version="1.1" viewbox="0 0 74.324997 16.7125" width="74.324997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7125)"> <g transform="translate(72,-58.63)"> <text transform="matrix(1,0,0,-1,-65.07,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.8766499" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.84,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.53,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="24.480873" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="31.720112" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-18.42,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>以标准的方式<S.。vg height="11.2" id="M82" style="vertical-align:-0.11285pt;width:16px;" version="1.1" viewbox="0 0 16 11.2" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2)"> <g transform="translate(72,-63.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.1125" id="M83" style="vertical-align:-2.29482pt;width:13.8875px;" version="1.1" viewbox="0 0 13.8875 14.1125" width="13.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1125)"> <g transform="translate(72,-60.71)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.84,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>，带有泊松括号<S.。vg height="15.1625" id="M84" style="vertical-align:-3.13504pt;width:105.275px;" version="1.1" viewbox="0 0 105.275 15.1625" width="105.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</T.S.pan> <tspan style="font-size: 12.50px; " x="6.00144" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-59.07,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-53.24,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-41.92,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-37.03,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-31.03,59.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> P.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.8748641" y="0"> B.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-16.34,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,1.95,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> </g> </g> </svg>．</p> <p>让我们讨论可以产生的古典变量<S.。vg height="10.475" id="M85" style="vertical-align:-0.0pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> </g> </g> </svg>矩阵。为此，我们首先研究它们的换向子。换向片的<S.。vg height="11.0625" id="M86" style="vertical-align:-0.0pt;width:16.5875px;" version="1.1" viewbox="0 0 16.5875 11.0625" width="16.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>不形成闭合的李代数，但产生<S.。vg height="13.45" id="M87" style="vertical-align:-2.21957pt;width:52.650002px;" version="1.1" viewbox="0 0 52.650002 13.45" width="52.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.S.pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> O.</T.S.pan> <tspan style="font-size: 12.50px; " x="15.978834" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="26.393833" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="31.595081" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="37.846581" y="0"> ）</T.S.pan> </text> </g> </g> </svg>洛伦兹发电机<S.。pan class="equation" id="EEq13"> <svg height="19.9" id="M88" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.9" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.9)"> <g transform="translate(72,-56.08)"> <text transform="matrix(1,0,0,-1,157.59,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="4.7800002" y="-2.51"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,169.71,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,175.54,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,188.09,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,192.98,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,197.77,56.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.S.pan> </text> <text transform="matrix(1,0,0,-1,207.74,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="30.732374" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,245.82,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,256.04,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="208.71001" y="0.20999999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="212.8735" y="0.20999999"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="219.125" y="0.20999999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="222.25075" y="0.20999999"> 4.</T.S.pan> <tspan style="font-size: 12.50px; " x="228.50224" y="0.20999999"> ）</T.S.pan> </text> </g> </g> </svg></span>它被指出的地方<S.。vg height="14.025" id="M89" style="vertical-align:-2.21957pt;width:160.45px;" version="1.1" viewbox="0 0 160.45 14.025" width="160.45" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.025)"> <g transform="translate(72,-60.78)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-50.92,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="20.092321" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="23.568155" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="29.819654" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="33.983154" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="38.146652" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-5.43,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,0.4,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,7.74,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,15.41,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,34.09,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,38.98,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,46.32,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,52.15,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> </g> </g> </svg>．套装<S.。vg height="11.0625" id="M90" style="vertical-align:-0.0pt;width:16.5875px;" version="1.1" viewbox="0 0 16.5875 11.0625" width="16.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="11.25" id="M91" style="vertical-align:-0.0pt;width:22.075001px;" version="1.1" viewbox="0 0 22.075001 11.25" width="22.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.25)"> <g transform="translate(72,-63)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> </g> </g> </svg>封闭的代数形式。除整流子(<a href="#EEq13">2．4</a>),有<S.。pan class="equation" id="EEq14"> <svg height="50.912498" id="M92" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.912498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.9125)"> <g transform="translate(72,-31.27)"> <text transform="matrix(1,0,0,-1,126.67,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="4.79" y="-2.51"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,138.79,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,149.02,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,161.57,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,167,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,171.79,56.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.S.pan> </text> <text transform="matrix(1,0,0,-1,181.75,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="24.27" y="-0.0099999998"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="28.433498" y="-0.0099999998"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,216.43,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,227.2,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,234.54,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,242.21,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,259.8,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="4.3935041" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,269.63,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,276.97,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,282.8,61.14)"> <tspan style="font-size: 12.50px; " x="-213.39999" y="27.33"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-208.61" y="24.82"> Γ</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="6.238997" y="0"> 那</T.S.pan> </text> <text transform="matrix(1,0,0,-1,81.53,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,91.75,36.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,104.3,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,114.62,33.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,119.41,31.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.S.pan> </text> <text transform="matrix(1,0,0,-1,129.37,36.32)"> <tspan style="font-size: 12.50px; " x="24.26" y="2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="30.120001" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,165.74,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,176.5,36.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,183.84,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="4.3935041" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,196.39,36.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,213.99,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,224.7,36.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,232.04,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="4.3935041" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,244.65,36.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,262.24,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="4.3935041" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,272.07,36.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,279.41,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,292.9,36.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,310.49,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="4.3935041" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,320.27,36.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,327.61,41.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,338.37,33.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="126.38" y="-14.7"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="130.5435" y="-14.7"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="136.795" y="-14.7"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="139.92075" y="-14.7"> 5.</T.S.pan> <tspan style="font-size: 12.50px; " x="146.17226" y="-14.7"> ）</T.S.pan> </text> </g> </g> </svg></span>代数(<a href="#EEq13">2．4</a>），（<a href="#EEq14">2．5</a>)可以等同于五维洛伦兹代数<S.。vg height="13.45" id="M93" style="vertical-align:-2.21957pt;width:52.650002px;" version="1.1" viewbox="0 0 52.650002 13.45" width="52.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.S.pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> O.</T.S.pan> <tspan style="font-size: 12.50px; " x="15.978834" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="26.393833" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="31.595081" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="37.846581" y="0"> ）</T.S.pan> </text> </g> </g> </svg>与发电机<S.。vg height="18.475" id="M94" style="vertical-align:-0.17555pt;width:27.7125px;" version="1.1" viewbox="0 0 27.7125 18.475" width="27.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.475)"> <g transform="translate(72,-57.22)"> <text transform="matrix(1,0,0,-1,-71.04,59.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.91000003" y="2.53"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.1,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> </g> </g> </svg><span class="equation" id="EEq15"> <svg height="29.5375" id="M95" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 29.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,29.5375)"> <g transform="translate(72,-48.37)"> <text transform="matrix(1,0,0,-1,45.31,52.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.6500001" y="-7.4499998"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.7399998" y="-4.9200001"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,59.9,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,73.12,57.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="6.1199999" y="-2.53"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.21" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,87.18,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,100.59,52.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,106.33,48.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</T.S.pan> </text> <text transform="matrix(1,0,0,-1,116.3,57.27)"> <tspan style="font-size: 12.50px; " x="24.26" y="4.9200001"> </T.S.pan> <tspan style="font-size: 12.50px; " x="31.629999" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,154.18,62.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,168.44,59.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.92000002" y="2.53"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,176.38,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.091392" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,192.79,57.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,210.38,62.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,225.11,59.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.91000003" y="2.53"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,233.05,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.091392" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,249,57.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,266.59,62.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.091392" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,280.67,59.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.92000002" y="2.53"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,288.6,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,305.2,57.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,322.8,62.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.091392" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,337.34,59.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.91000003" y="2.53"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,345.28,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,358.63,52.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="9.6899996" y="-4.9200001"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="106.12" y="-4.71"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="110.2835" y="-4.71"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="116.535" y="-4.71"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="119.66075" y="-4.71"> 6.</T.S.pan> <tspan style="font-size: 12.50px; " x="125.91225" y="-4.71"> ）</T.S.pan> </text> </g> </g> </svg></span>假设<S.。vg height="18.7125" id="M96" style="vertical-align:-0.17555pt;width:59.787498px;" version="1.1" viewbox="0 0 59.787498 18.7125" width="59.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7125)"> <g transform="translate(72,-57.03)"> <text transform="matrix(1,0,0,-1,-71.95,57.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,62.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.31,57.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</T.S.pan> <tspan style="font-size: 12.50px; " x="12.95" y="-2.54"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-34.42,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="16.0625" id="M97" style="vertical-align:-0.17555pt;width:65.3125px;" version="1.1" viewbox="0 0 65.3125 16.0625" width="65.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.0625)"> <g transform="translate(72,-59.15)"> <text transform="matrix(1,0,0,-1,-71.95,59.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.61,64.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-50.92,59.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</T.S.pan> <tspan style="font-size: 12.50px; " x="12.95" y="-2.54"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-30.03,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> </g> </g> </svg>．</p> <p>从古典机械模型开始到达代数，我们介绍了自由度自由度的十维“相位”空间，<S.。vg height="13.85" id="M98" style="vertical-align:-0.13794pt;width:19.237499px;" version="1.1" viewbox="0 0 19.237499 13.85" width="19.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.85)"> <g transform="translate(72,-60.92)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.725" id="M99" style="vertical-align:-0.16302pt;width:18.299999px;" version="1.1" viewbox="0 0 18.299999 13.725" width="18.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>，配有泊松支架<S.。pan class="equation" id="EEq16"> <svg height="19.924999" id="M100" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.925)"> <g transform="translate(72,-56.06)"> <text transform="matrix(1,0,0,-1,159.01,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.1900001" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,174.71,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,181.49,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,194.3,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,201.24,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,208.43,56.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> P.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.8748641" y="0"> B.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,223.11,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,241.4,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,254.62,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="210.13" y="0.20999999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="214.2935" y="0.20999999"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="220.545" y="0.20999999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="223.67075" y="0.20999999"> 7.</T.S.pan> <tspan style="font-size: 12.50px; " x="229.92226" y="0.20999999"> ）</T.S.pan> </text> </g> </g> </svg></span>然后泊松括号的数量<S.。pan class="equation" id="EEq17"> <svg height="19.375" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.375)"> <g transform="translate(72,-56.5)"> <text transform="matrix(1,0,0,-1,142.98,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,151.23,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,167.92,61.11)"> <tspan style="font-size: 12.50px; " x="20.370001" y="2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="26.219999" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,202.66,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,209.43,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,217.03,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,226.75,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,246.61,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,253.55,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,261.15,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,267.92,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="196.83" y="-2.52"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="200.9935" y="-2.52"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="207.245" y="-2.52"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="210.37074" y="-2.52"> 8.</T.S.pan> <tspan style="font-size: 12.50px; " x="216.62225" y="-2.52"> ）</T.S.pan> </text> </g> </g> </svg></span>读<S.。pan class="equation" id="EEq18"> <svg height="19.924999" id="M102" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.925)"> <g transform="translate(72,-56.06)"> <text transform="matrix(1,0,0,-1,46.88,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.1900001" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,62.32,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,75.53,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,88.99,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,102.41,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,109.6,56.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> P.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.8748641" y="0"> B.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,124.28,61.11)"> <tspan style="font-size: 12.50px; " x="20.379999" y="2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="26.23" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,156.76,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,170.11,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,178.36,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.091392" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,194.77,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,212.37,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,226.19,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,234.44,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.091392" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,250.38,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,267.97,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.091392" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,281.14,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,289.39,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,305.99,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,323.58,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.091392" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,337.22,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,345.47,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,358.81,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="105.94" y="-2.3"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="110.1035" y="-2.3"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="116.355" y="-2.3"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="119.48075" y="-2.3"> 9.</T.S.pan> <tspan style="font-size: 12.50px; " x="125.73225" y="-2.3"> ）</T.S.pan> </text> </g> </g> </svg></span>下面我们使用分解<S.。pan class="equation" id="EEq19"> <svg height="19.8125" id="M103" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.8125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8125)"> <g transform="translate(72,-56.15)"> <text transform="matrix(1,0,0,-1,49.03,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,57.28,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,73.97,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="17.889999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,100.11,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,110.32,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,123.78,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,134,58.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="21.360001" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="27.209999" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,169.47,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,178.72,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,196.35,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,207.41,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,225.7,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,230.58,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,248.21,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,259.28,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,301.45,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,312.07,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,329.98,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.1264" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,341.35,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,351.42,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,356.66,58.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="101.83" y="-2.7"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="105.9935" y="-2.7"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="112.245" y="-2.7"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="115.37075" y="-2.7"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="121.62225" y="-2.7"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="127.87375" y="-2.7"> ）</T.S.pan> </text> </g> </g> </svg></span></p> <p>这个变换的雅可比矩阵<S.。vg height="16.4375" id="M104" style="vertical-align:-2.21957pt;width:109.525px;" version="1.1" viewbox="0 0 109.525 16.4375" width="109.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.4375)"> <g transform="translate(72,-58.85)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-59.27,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-52.5,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-39.69,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-32.75,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> →</T.S.pan> <tspan style="font-size: 12.50px; " x="26.856443" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,2.36,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> </g> </g> </svg>它的秩等于7。十个函数中只有七个<S.。vg height="16.4375" id="M105" style="vertical-align:-2.21957pt;width:64.025002px;" version="1.1" viewbox="0 0 64.025002 16.4375" width="64.025002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.4375)"> <g transform="translate(72,-58.85)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="6.2751842" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-50.48,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.678042" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="17.87929" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="25.481113" y="0"> ）</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="10.925" id="M106" style="vertical-align:-0.30096pt;width:42.224998px;" version="1.1" viewbox="0 0 42.224998 10.925" width="42.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.427982" y="0"> <</T.S.pan> <tspan style="font-size: 12.50px; " x="24.46837" y="0"> </T.S.pan> </text> </g> </g> </svg>，是独立量。它们可以分开如下。按建造计算，工程量(<a href="#EEq17">2．8</a>)服从身份<S.。pan class="equation" id="EEq20"> <svg height="33.275002" id="M107" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 33.275002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,33.275)"> <g transform="translate(72,-45.38)"> <text transform="matrix(1,0,0,-1,72.96,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,78.84,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="9.7147198" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="14.650848" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,98.88,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,107.13,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.8800001" y="8.1300001"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,116.9,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,123.65,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="4.9361281" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,137.44,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="33.458027" y="0"> ⟺</T.S.pan> <tspan style="font-size: 12.50px; " x="56.613583" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,202.31,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,212.93,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="18.860001" y="-7.25"> 1</T.S.pan> </text> <g> <path d="m 226.16,59.37 17.51,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,226.16,45.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,234.42,50.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,246.95,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,261.05,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,268.65,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,276.9,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,288.48,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,308.08,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,316.88,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,325.13,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,332.73,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="125.76" y="-1.83"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="129.92349" y="-1.83"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="136.175" y="-1.83"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="139.30075" y="-1.83"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="145.55225" y="-1.83"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="151.80374" y="-1.83"> ）</T.S.pan> </text> </g> </g> </svg></span>也就是三维向量<S.。vg height="10.6875" id="M108" style="vertical-align:-0.0pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.6875" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>可以通过<S.。vg height="15.4875" id="M109" style="vertical-align:-1.20384pt;width:14.0375px;" version="1.1" viewbox="0 0 14.0375 15.4875" width="14.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4875)"> <g transform="translate(72,-59.61)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="10.925" id="M110" style="vertical-align:-0.1881pt;width:15.75px;" version="1.1" viewbox="0 0 15.75 10.925" width="15.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>作为<S.。pan class="equation" id="EEq21"> <svg height="33.275002" id="M111" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 33.275002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,33.275)"> <g transform="translate(72,-45.38)"> <text transform="matrix(1,0,0,-1,166,56.25)"> <tspan style="font-size: 12.50px; " x="31.360001" y="-7.25"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.503" y="0"> =</T.S.pan> </text> <g> <path d="m 191.74,59.37 17.5,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,191.74,45.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,199.99,50.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,210.43,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,216.69,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,224.34,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</T.S.pan> <tspan style="font-size: 12.50px; " x="10.777586" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="23.280586" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="234.14999" y="0.69"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="238.31349" y="0.69"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="244.565" y="0.69"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="247.69075" y="0.69"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="253.94225" y="0.69"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="260.19376" y="0.69"> ）</T.S.pan> </text> </g> </g> </svg></span>此外,<S.。vg height="16.4375" id="M112" style="vertical-align:-2.21957pt;width:54.337502px;" version="1.1" viewbox="0 0 54.337502 16.4375" width="54.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.4375)"> <g transform="translate(72,-58.85)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-59.27,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-52.5,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-39.69,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-32.75,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> </g> </g> </svg>-space可以由坐标参数化<S.。vg height="14.0875" id="M113" style="vertical-align:-0.15048pt;width:23.200001px;" version="1.1" viewbox="0 0 23.200001 14.0875" width="23.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0875)"> <g transform="translate(72,-60.73)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.9625" id="M114" style="vertical-align:-0.15048pt;width:19.9375px;" version="1.1" viewbox="0 0 19.9375 13.9625" width="19.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.9375" id="M115" style="vertical-align:-0.13794pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 13.9375" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9375)"> <g transform="translate(72,-60.85)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.075" id="M116" style="vertical-align:-0.13794pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 14.075" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.1" id="M117" style="vertical-align:-0.16302pt;width:15.725px;" version="1.1" viewbox="0 0 15.725 14.1" width="15.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1)"> <g transform="translate(72,-60.72)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>．我们还不能量化变量，因为这会导致出现一些运算符<S.。vg height="15.575" id="M118" style="vertical-align:-0.17555pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 15.575" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.575)"> <g transform="translate(72,-59.54)"> <text transform="matrix(1,0,0,-1,-71.19,59.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.75018001" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="15.7125" id="M119" style="vertical-align:-0.17555pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 15.7125" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.7125)"> <g transform="translate(72,-59.43)"> <text transform="matrix(1,0,0,-1,-71.19,59.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.75018001" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="15.7375" id="M120" style="vertical-align:-0.17555pt;width:15.725px;" version="1.1" viewbox="0 0 15.725 15.7375" width="15.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.7375)"> <g transform="translate(72,-59.41)"> <text transform="matrix(1,0,0,-1,-71.65,59.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-0.30007201" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>，在狄拉克理论中没有，也不是描述自旋所必需的。为了避免这个问题，我们去掉变量<S.。vg height="13.9375" id="M121" style="vertical-align:-0.13794pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 13.9375" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9375)"> <g transform="translate(72,-60.85)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.075" id="M122" style="vertical-align:-0.13794pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 14.075" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.1" id="M123" style="vertical-align:-0.16302pt;width:15.725px;" version="1.1" viewbox="0 0 15.725 14.1" width="15.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1)"> <g transform="translate(72,-60.72)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>，将我们的模型限制在十维相空间的七维曲面上<S.。vg height="13.85" id="M124" style="vertical-align:-0.13794pt;width:19.237499px;" version="1.1" viewbox="0 0 19.237499 13.85" width="19.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.85)"> <g transform="translate(72,-60.92)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.725" id="M125" style="vertical-align:-0.16302pt;width:18.299999px;" version="1.1" viewbox="0 0 18.299999 13.725" width="18.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．唯一的<S.。vg height="13.45" id="M126" style="vertical-align:-2.21957pt;width:52.650002px;" version="1.1" viewbox="0 0 52.650002 13.45" width="52.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.S.pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> O.</T.S.pan> <tspan style="font-size: 12.50px; " x="15.978834" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="26.393833" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="31.595081" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="37.846581" y="0"> ）</T.S.pan> </text> </g> </g> </svg>二次不变量可以由<S.。vg height="15.875" id="M127" style="vertical-align:-1.76814pt;width:43.924999px;" version="1.1" viewbox="0 0 43.924999 15.875" width="43.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.66,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-43.85,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>是<S.。vg height="17.575001" id="M128" style="vertical-align:-3.13504pt;width:38.349998px;" version="1.1" viewbox="0 0 38.349998 17.575001" width="38.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.575)"> <g transform="translate(72,-57.94)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.66,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-48.15,57.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="17.575001" id="M129" style="vertical-align:-3.13504pt;width:37.200001px;" version="1.1" viewbox="0 0 37.200001 17.575001" width="37.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.575)"> <g transform="translate(72,-57.94)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.66,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-49.06,57.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="17.575001" id="M130" style="vertical-align:-3.13504pt;width:36.0625px;" version="1.1" viewbox="0 0 36.0625 17.575001" width="36.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.575)"> <g transform="translate(72,-57.94)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.57,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-49.97,57.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．我们在等方程中选择的表面<S.。pan class="equation" id="EEq22"> <svg height="47.8125" id="M131" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 47.8125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,47.8125)"> <g transform="translate(72,-33.75)"> <text transform="matrix(1,0,0,-1,170,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,178.51,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,185.29,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,193.8,57.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,203.35,61.11)"> <tspan style="font-size: 12.50px; " x="-59.029999" y="23.559999"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="24.068275" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="36.108665" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="42.360165" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="255.14" y="-0.41999999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="259.3035" y="-0.41999999"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="265.55499" y="-0.41999999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="268.68076" y="-0.41999999"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="274.93225" y="-0.41999999"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="281.18375" y="-0.41999999"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,152.83,42.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,159.61,37.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,167.21,34.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,177.45,37.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="43.42292" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,228.48,42.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,235.25,37.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,242.86,34.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,253.1,37.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="205.39" y="-0.41999999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="209.5535" y="-0.41999999"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="215.80499" y="-0.41999999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="218.93076" y="-0.41999999"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="225.18225" y="-0.41999999"> 4.</T.S.pan> <tspan style="font-size: 12.50px; " x="231.43375" y="-0.41999999"> ）</T.S.pan> </text> </g> </g> </svg></span> <svg height="11.0625" id="M133" style="vertical-align:-0.30096pt;width:91.150002px;" version="1.1" viewbox="0 0 91.150002 11.0625" width="91.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.715551" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="24.755939" y="0"> C</T.S.pan> <tspan style="font-size: 12.50px; " x="30.307272" y="0"> O.</T.S.pan> <tspan style="font-size: 12.50px; " x="36.558773" y="0"> N</T.S.pan> <tspan style="font-size: 12.50px; " x="42.810272" y="0"> S.</T.S.pan> <tspan style="font-size: 12.50px; " x="47.586418" y="0"> T.</T.S.pan> <tspan style="font-size: 12.50px; " x="54.525581" y="0"> ></T.S.pan> <tspan style="font-size: 12.50px; " x="66.565971" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>．的数量<S.。vg height="14.0875" id="M134" style="vertical-align:-0.15048pt;width:23.200001px;" version="1.1" viewbox="0 0 23.200001 14.0875" width="23.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0875)"> <g transform="translate(72,-60.73)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.9625" id="M135" style="vertical-align:-0.15048pt;width:19.9375px;" version="1.1" viewbox="0 0 19.9375 13.9625" width="19.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>形成一个自旋空间曲面的坐标系。我们可以量化它们而不是初始变量<S.。vg height="13.85" id="M136" style="vertical-align:-0.13794pt;width:19.237499px;" version="1.1" viewbox="0 0 19.237499 13.85" width="19.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.85)"> <g transform="translate(72,-60.92)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.725" id="M137" style="vertical-align:-0.16302pt;width:18.299999px;" version="1.1" viewbox="0 0 18.299999 13.725" width="18.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．</p> <p>根据(<a href="#EEq1">1．1</a>），（<a href="#EEq15">2．6</a>），（<a href="#EEq18">2．9</a>），量化替换古典变量<S.。vg height="14.0875" id="M138" style="vertical-align:-0.15048pt;width:23.200001px;" version="1.1" viewbox="0 0 23.200001 14.0875" width="23.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0875)"> <g transform="translate(72,-60.73)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="11.4375" id="M139" style="vertical-align:-0.15048pt;width:23.2125px;" version="1.1" viewbox="0 0 23.2125 11.4375" width="23.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.4375)"> <g transform="translate(72,-62.85)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> </g> </g> </svg>在<S.。vg height="10.475" id="M140" style="vertical-align:-0.0pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> </g> </g> </svg>矩阵<S.。pan class="equation" id="EEq24"> <svg height="18.5875" id="M141" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5875)"> <g transform="translate(72,-57.13)"> <text transform="matrix(1,0,0,-1,126.55,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,134.8,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,148.48,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟶</T.S.pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="30.38229" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,186.21,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,192.04,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,225.43,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,239.12,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟶</T.S.pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="30.38229" y="0"> Γ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,276.85,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,287.07,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="171.42" y="-0.50999999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="175.5835" y="-0.50999999"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="181.83499" y="-0.50999999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="184.96075" y="-0.50999999"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="191.21225" y="-0.50999999"> 5.</T.S.pan> <tspan style="font-size: 12.50px; " x="197.46375" y="-0.50999999"> ）</T.S.pan> </text> </g> </g> </svg></span>这意味着，狄拉克方程可以由约束条件产生(我们重申这一点<S.。vg height="16.674999" id="M142" style="vertical-align:-2.21957pt;width:145.5px;" version="1.1" viewbox="0 0 145.5 16.674999" width="145.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.675)"> <g transform="translate(72,-58.66)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-50.02,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-19.05,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-14.18,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-6.58,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,2.03,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,21.89,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,27.72,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,35.32,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,40.19,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> </g> </g> </svg>）<S.。pan class="equation" id="EEq25"> <svg height="19.8125" id="M143" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.8125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8125)"> <g transform="translate(72,-56.15)"> <text transform="matrix(1,0,0,-1,163.02,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,169.13,57.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,174.96,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,183.21,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,196.2,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="20.204847" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="25.393593" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="36.108665" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="48.149052" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="54.400555" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="262.29001" y="-0.02"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="266.45349" y="-0.02"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="272.70499" y="-0.02"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="275.83075" y="-0.02"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="282.08224" y="-0.02"> 6.</T.S.pan> <tspan style="font-size: 12.50px; " x="288.33374" y="-0.02"> ）</T.S.pan> </text> </g> </g> </svg></span></p> <p>综上所述，为了描述相对论自旋，我们需要一个包含狄拉克约束(<a href="#EEq22">2.13</a>），（<a href="#EEq22">2.14</a>），（<a href="#EEq25">2.16</a>）在Hamiltonian的配方中。</p> <h4 id="dynamical-realization">3.动态实现</h4> <p>上面提出的结构的一种可能的动态实现是由以下提供的<S.。vg height="10.875" id="M144" style="vertical-align:-0.15048pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.875" width="35.637501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.875)"> <g transform="translate(72,-63.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.114927" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="22.155315" y="0"> 4.</T.S.pan> </text> </g> </g> </svg>Poincare-Invariant Lagrangian<S.。pan class="equation" id="EEq26"> <svg height="34.712502" id="M145" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 34.712502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,34.7125)"> <g transform="translate(72,-44.23)"> <text transform="matrix(1,0,0,-1,-52.37,56.16)"> <tspan style="font-size: 12.50px; " x="39.34" y="-7.25"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.315455" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="24.355844" y="0"> −</T.S.pan> </text> <g> <path d="m -18.24,59.28 16.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-18.24,47.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-6.43,44.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,1.72,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.7399998" y="-2.4100001"> </T.S.pan> <tspan style="font-size: 12.50px; " x="17.91" y="-4.9200001"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="11.595985" y="-4.9200001"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,20.19,61.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,28.8,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,45.71,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,50.58,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,59.09,61.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,64.92,53.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,70.77,63.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,78.43,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.34" y="2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="17.190001" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,101.18,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,106.06,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,114.57,61.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,119.45,53.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,125.3,63.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,130.17,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.5200005" y="-4.9200001"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="21.059999" y="-12.17"> </T.S.pan> <tspan style="font-size: 12.50px; " x="28.386759" y="-12.17"> </T.S.pan> <tspan style="font-size: 12.50px; " x="37.263889" y="-12.17"> </T.S.pan> <tspan style="font-size: 12.50px; " x="42.452633" y="-12.17"> ℏ</T.S.pan> </text> <g> <path d="m 151.23,59.28 28.64,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,155.73,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,170.5,50.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,183.85,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="13.08" y="-7.25"> 1</T.S.pan> </text> <g> <path d="m 196.39,59.28 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,196.39,47.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.62" y="-6.2399998"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.408649" y="-6.2399998"> </T.S.pan> <tspan style="font-size: 12.50px; " x="27.57" y="-8.75"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="21.255985" y="-8.75"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,224.52,61.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,233.13,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,250.04,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,254.91,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,263.42,61.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,269.25,53.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.07" y="-2.51"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="7.9432902" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,285.7,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,294.31,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,311.22,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,316.09,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,324.61,61.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,336.61,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-7.1267099" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,337.99,61.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,342.87,53.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="7.5700002" y="-2.51"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="18.897718" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,367.34,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,374.3,53.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,388.67,61.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,395.44,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,403.95,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,413.51,56.16)"> <tspan style="font-size: 12.50px; " x="20.59" y="2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="28.530001" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="51.240002" y="1.17"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="55.4035" y="1.17"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="61.654999" y="1.17"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="64.780746" y="1.17"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="71.032249" y="1.17"> ）</T.S.pan> </text> </g> </g> </svg></span>写在配置空间上<S.。vg height="11.2" id="M146" style="vertical-align:-0.11285pt;width:16px;" version="1.1" viewbox="0 0 16 11.2" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2)"> <g transform="translate(72,-63.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="11.225" id="M147" style="vertical-align:-0.13794pt;width:18.049999px;" version="1.1" viewbox="0 0 18.049999 11.225" width="18.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.225)"> <g transform="translate(72,-63.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.075" id="M148" style="vertical-align:-0.13794pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 14.075" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="11.05" id="M149" style="vertical-align:-3.2316pt;width:11.1px;" version="1.1" viewbox="0 0 11.1 11.05" width="11.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-66.39,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="6.9875002" id="M150" style="vertical-align:-0.13794pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>,在那里<S.。vg height="11.05" id="M151" style="vertical-align:-3.2316pt;width:11.1px;" version="1.1" viewbox="0 0 11.1 11.05" width="11.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-66.39,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="6.9875002" id="M152" style="vertical-align:-0.13794pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>是辅助变量。的变量<S.。vg height="14.075" id="M153" style="vertical-align:-0.13794pt;width:16.862499px;" version="1.1" viewbox="0 0 16.862499 14.075" width="16.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="11.05" id="M154" style="vertical-align:-3.2316pt;width:11.1px;" version="1.1" viewbox="0 0 11.1 11.05" width="11.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-66.39,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="6.9875002" id="M155" style="vertical-align:-0.13794pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>是庞加莱变换下的标量。其余的变量根据规则进行转换<S.。pan class="equation" id="EEq27"> <svg height="16.65" id="M156" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.65" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.65)"> <g transform="translate(72,-58.68)"> <text transform="matrix(1,0,0,-1,116.4,63.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.8766499" y="0"> '</T.S.pan> </text> <text transform="matrix(1,0,0,-1,126.89,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,136.19,63.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> Λ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,157.01,68.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.8200002" y="8.2700005"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,167.73,63.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,174.6,68.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,182.27,63.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,199.89,68.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,205.72,63.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="33.645573" y="0"> '</T.S.pan> </text> <text transform="matrix(1,0,0,-1,242.98,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,252.28,63.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> Λ</T.S.pan> </text> <text transform="matrix(1,0,0,-1,273.1,68.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.8299999" y="8.2700005"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,283.82,63.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,292.33,68.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,297.23,63.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="167.52" y="0.52999997"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="171.6835" y="0.52999997"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="177.935" y="0.52999997"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="181.06075" y="0.52999997"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="187.31226" y="0.52999997"> ）</T.S.pan> </text> </g> </g> </svg></span>理论的局部对称性形成了由重参数化构成的双参数群<S.。pan class="equation" id="EEq28"> <svg height="19.375" id="M157" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.375)"> <g transform="translate(72,-56.5)"> <text transform="matrix(1,0,0,-1,54.59,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,67.76,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,77.06,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="25.393593" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="19.092081" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,103.02,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,108.85,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="31.420038" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,148.79,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,159.04,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="26.206287" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="19.092081" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,186.64,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,193.41,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="31.420038" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,230.4,57.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,237.09,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.04" y="2.51"> </T.S.pan> <tspan style="font-size: 12.50px; " x="17.889999" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="24.941692" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,267.6,57.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,270.82,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,276.67,68.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.S.pan> </text> <text transform="matrix(1,0,0,-1,279.36,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="31.420038" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="42.22263" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="54.26302" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="58.426517" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="65.47821" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="72.817474" y="0"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,356.35,66.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ．</T.S.pan> </text> <text transform="matrix(1,0,0,-1,359.04,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="105.71" y="-0.0099999998"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="109.8735" y="-0.0099999998"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="116.125" y="-0.0099999998"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="119.25075" y="-0.0099999998"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="125.50225" y="-0.0099999998"> ）</T.S.pan> </text> </g> </g> </svg></span>以及参数的局部变换<S.。vg height="13.45" id="M158" style="vertical-align:-2.21957pt;width:25.875px;" version="1.1" viewbox="0 0 25.875 13.45" width="25.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.8639069" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="10.027406" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="16.428942" y="0"> ）</T.S.pan> </text> </g> </g> </svg>(下面我们已经指出<S.。vg height="14.6" id="M159" style="vertical-align:-3.13504pt;width:117.05px;" version="1.1" viewbox="0 0 117.05 14.6" width="117.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> ≡</T.S.pan> <tspan style="font-size: 12.50px; " x="28.144253" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="22.492897" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-43.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-39.02,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.6395731" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="19.992296" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="24.155796" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="30.407295" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="33.883129" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="40.134628" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="44.29813" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,10.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,21.53,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-5.8013921" y="0"> </T.S.pan> </text> </g> </g> </svg>）<S.。pan class="equation" id="EEq29"> <svg height="69.4375" id="M160" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 69.4375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,69.4375)"> <g transform="translate(72,-16.45)"> <text transform="matrix(1,0,0,-1,84.11,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,97.27,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,106.57,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="43.42292" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="49.711929" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,164.8,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,175.05,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="19.00456" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,202.58,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,209.35,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="31.420038" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="42.235134" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="54.26302" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="61.239693" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="68.578957" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="83.757599" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="90.046608" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,304.97,57.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,313.31,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="-224.7" y="32.360001"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-218.411" y="32.360001"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,100.47,25.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,108.81,28.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="27.581617" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,141.96,25.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,149.61,28.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="12.54" y="-9.1400003"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,167.71,34.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <g> <path d="m 162.15,31.88 10.44,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,163.7,20)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="16.450001" y="-11.48"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="10.08" y="-8.75"> </T.S.pan> <tspan style="font-size: 12.50px; " x="17.056673" y="-8.75"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="42.187702" y="-8.75"> </T.S.pan> <tspan style="font-size: 12.50px; " x="48.476711" y="-8.75"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,217.75,25.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,226.09,28.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="26.856443" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,258.51,25.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,263.39,28.75)"> <tspan style="font-size: 12.50px; " x="21.09" y="7.3299999"> </T.S.pan> <tspan style="font-size: 12.50px; " x="32.189999" y="-9.1400003"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> −</T.S.pan> </text> <text transform="matrix(1,0,0,-1,301.15,34.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,312.38,40.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.3600001" y="2.73"> </T.S.pan> </text> <g> <path d="m 295.06,31.88 18.46,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,295.06,19.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,308.65,23.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,314.72,21.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,324.09,45.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⋅</T.S.pan> </text> <text transform="matrix(1,0,0,-1,327.1,28.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="137.64999" y="-12.35"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="141.81349" y="-12.35"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="148.065" y="-12.35"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="151.19075" y="-12.35"> 4.</T.S.pan> <tspan style="font-size: 12.50px; " x="157.44225" y="-12.35"> ）</T.S.pan> </text> </g> </g> </svg></span>局部对称保证了一类约束的出现(<a href="#EEq22">2.13</a>），（<a href="#EEq25">2.16</a>）.</p> <p>奇怪的是，这种行为几乎可以以五维的形式重写。的确，在改变之后<S.。vg height="15.125" id="M161" style="vertical-align:-3.25793pt;width:61.662498px;" version="1.1" viewbox="0 0 61.662498 15.125" width="61.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.125)"> <g transform="translate(72,-59.9)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-60.91,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.08,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.540509" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="17.754259" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-31.76,60.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-26.89,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> </g> </g> </svg> <svg height="7.125" id="M162" style="vertical-align:-0.0pt;width:19.8125px;" version="1.1" viewbox="0 0 19.8125 7.125" width="19.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.125)"> <g transform="translate(72,-66.3)"> <text transform="matrix(1,0,0,-1,-69.87,66.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> →</T.S.pan> </text> </g> </g> </svg> <svg height="17.9625" id="M163" style="vertical-align:-3.25793pt;width:67.175003px;" version="1.1" viewbox="0 0 67.175003 17.9625" width="67.175003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9625)"> <g transform="translate(72,-57.63)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="10.827598" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-60.91,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.08,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="11.87785" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-43,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-38.12,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="11.815335" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-27.35,57.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-22.47,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> </g> </g> </svg>,在那里<S.。vg height="14.9625" id="M164" style="vertical-align:-3.13504pt;width:123.825px;" version="1.1" viewbox="0 0 123.825 14.9625" width="123.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9625)"> <g transform="translate(72,-60.03)"> <text transform="matrix(1,0,0,-1,-65.27,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.6766019" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.77,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-36.86,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-28.25,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="15.50372" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-7.18,60.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-2.31,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.815095" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="14.978594" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,21.19,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="17.8125" id="M165" style="vertical-align:-3.13504pt;width:98.625px;" version="1.1" viewbox="0 0 98.625 17.8125" width="98.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8125)"> <g transform="translate(72,-57.75)"> <text transform="matrix(1,0,0,-1,-65.27,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.6766019" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.73,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="24.768442" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-26.4,57.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-21.52,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.802592" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="14.966091" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,1.97,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.75" id="M166" style="vertical-align:-3.25793pt;width:100.2375px;" version="1.1" viewbox="0 0 100.2375 14.75" width="100.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-65.34,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.601584" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-66.39,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-58.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-40.44,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-32.78,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="15.491217" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-11.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-6.84,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.815095" y="0"> ）</T.S.pan> </text> </g> </g> </svg>,它读取<S.。pan class="equation" id="EEq30"> <svg height="52.637501" id="M167" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 52.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,52.6375)"> <g transform="translate(72,-29.89)"> <text transform="matrix(1,0,0,-1,41.83,47.72)"> <tspan style="font-size: 12.50px; 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" x="15.914915" y="-2.52"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,116.63,52.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,123.4,45.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,129.25,55.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,136.91,47.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="21.700001" y="-8.0600004"> </T.S.pan> <tspan style="font-size: 12.50px; " x="34.23" y="-10.57"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="27.553398" y="-10.57"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,171.34,63.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,176.21,55.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,182.06,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <g> <path d="m 149.45,50.84 46.65,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,149.45,34.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,161.26,31.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,166.14,31.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,180.5,37.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,185.38,31.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,191.23,42.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,197.3,45.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="12.98" y="-2.52"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="5.8532901" y="-2.52"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,211.66,52.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,218.44,45.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,224.29,55.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,231.94,47.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="12.54" y="-9.1400003"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,250.04,53.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,254.92,56.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.8771296" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="14.065875" y="0"> ℏ</T.S.pan> </text> <g> <path d="m 244.48,50.84 31.74,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,261.15,37.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.6640992" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,261.35,41.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,280.2,47.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,297.1,44.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,304.06,45.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,318.43,52.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,325.2,47.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,333.72,44.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,343.27,47.72)"> <tspan style="font-size: 12.50px; " x="20.59" y="2.52"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="28.530001" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="121.48" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="125.6435" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="131.895" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="135.02075" y="0"> 5.</T.S.pan> <tspan style="font-size: 12.50px; " x="141.27225" y="0"> ）</T.S.pan> </text> </g> </g> </svg></span>协助衍生物的地方<S.。vg height="20.0375" id="M168" style="vertical-align:-3.25793pt;width:116.025px;" version="1.1" viewbox="0 0 116.025 20.0375" width="116.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.0375)"> <g transform="translate(72,-55.97)"> <text transform="matrix(1,0,0,-1,-71.95,59.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="16.729013" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="10.064915" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.01,64.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-44.76,59.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="18.35" y="-2.3499999"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="18.709999" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="12.045901" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-25.85,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-16.3,59.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="17.954308" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="11.352724" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,0.61,56.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,5.49,59.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,14,64.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>(这个变化是拉格朗日公式中第二类约束的转换的一个例子[<a href="#B17">25</a>])。</p> <p><span class="statement" id="head1"><span class="statement-title"><i class="statement-title">正则量子化</i></span><br>在哈密顿的形式主义中，行动意味着所需的约束（<a href="#EEq22">2.13</a>），（<a href="#EEq22">2.14</a>），（<a href="#EEq25">2.16</a>）.约束（<a href="#EEq22">2.13</a>），（<a href="#EEq22">2.14</a>）通过从泊松到Dirac支架的过渡可以考虑，之后他们从考虑中省略了[<a href="#B14">17</a>那<a href="#B16">26</a>］．第一类约束(<a href="#EEq25">2.16</a>)作用于状态向量，得到狄拉克方程。在结果中，模型的正则量子化导致所需的量子图像。<br>我们现在讨论经典理论的一些性质，并确认它们与半经典极限相一致[<a href="#B2">3.</a>那<a href="#B18">27</a>那<a href="#B19">28</a>狄拉克方程的。</S.。pan></p> <p><span class="statement" id="head2"><span class="statement-title"><i class="statement-title">运动方程</i></span><br>辅助变量<S.。vg height="11.05" id="M169" style="vertical-align:-3.2316pt;width:11.1px;" version="1.1" viewbox="0 0 11.1 11.05" width="11.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; 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" x="27.620001" y="-7.25"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="14.390953" y="0"> =</T.S.pan> </text> <g> <path d="m 150.29,59.37 6.26,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,150.29,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,165.34,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,172.12,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,179.72,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,189.27,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="12.54" y="-7.25"> 1</T.S.pan> </text> <g> <path d="m 201.81,59.37 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,201.81,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="9.5299997" y="-6.2399998"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.38" y="-8.7600002"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,223.31,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,229.13,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,237.39,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,250.37,56.25)"> <tspan style="font-size: 12.50px; " x="32.650002" y="2.52"> </T.S.pan> <tspan style="font-size: 12.50px; " x="40.580002" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="20.217352" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="25.406096" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="214.38" y="-0.34999999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="218.5435" y="-0.34999999"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="224.795" y="-0.34999999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="227.92075" y="-0.34999999"> 6.</T.S.pan> <tspan style="font-size: 12.50px; " x="234.17226" y="-0.34999999"> ）</T.S.pan> </text> </g> </g> </svg></span>自从<S.。vg height="13.85" id="M172" style="vertical-align:-0.13794pt;width:19.237499px;" version="1.1" viewbox="0 0 19.237499 13.85" width="19.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.85)"> <g transform="translate(72,-60.92)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.44,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="13.875" id="M173" style="vertical-align:-0.16302pt;width:18.0875px;" version="1.1" viewbox="0 0 18.0875 13.875" width="18.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.875)"> <g transform="translate(72,-60.9)"> <text transform="matrix(1,0,0,-1,-71.95,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-64.35,66.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>不是<S.。vg height="7.1875" id="M174" style="vertical-align:-0.13794pt;width:7.4749999px;" version="1.1" viewbox="0 0 7.4749999 7.1875" width="7.4749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>-不变变量，它们的运动方程没有多大意义。我们写出运动方程<S.。vg height="7.1875" id="M175" style="vertical-align:-0.13794pt;width:7.4749999px;" version="1.1" viewbox="0 0 7.4749999 7.1875" width="7.4749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>-Invariant数量<S.。vg height="11.2" id="M176" style="vertical-align:-0.11285pt;width:16px;" version="1.1" viewbox="0 0 16 11.2" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2)"> <g transform="translate(72,-63.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="12.925" id="M177" style="vertical-align:-4.74141pt;width:15.05px;" version="1.1" viewbox="0 0 15.05 12.925" width="15.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.0875" id="M178" style="vertical-align:-0.15048pt;width:23.200001px;" version="1.1" viewbox="0 0 23.200001 14.0875" width="23.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0875)"> <g transform="translate(72,-60.73)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="11.4375" id="M179" style="vertical-align:-0.15048pt;width:23.2125px;" version="1.1" viewbox="0 0 23.2125 11.4375" width="23.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.4375)"> <g transform="translate(72,-62.85)"> <text transform="matrix(1,0,0,-1,-71.95,63.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> </g> </g> </svg><span class="equation" id="EEq32"> <svg height="140.5125" id="M180" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 140.5125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,140.5125)"> <g transform="translate(72,40.41)"> <text transform="matrix(1,0,0,-1,186.51,54.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.3015118" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,187.07,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,196.38,54.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="13.23" y="-7.25"> 1</T.S.pan> </text> <g> <path d="m 209.61,57.57 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,209.61,45.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,225.31,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,235.51,54.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="-57.700001" y="32.689999"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-64.699997" y="35.23"> </T.S.pan> <tspan style="font-size: 12.50px; " x="229.24001" y="-1.25"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="233.4035" y="-1.25"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="239.655" y="-1.25"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="242.78075" y="-1.25"> 7.</T.S.pan> <tspan style="font-size: 12.50px; " x="249.03224" y="-1.25"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,179.06,24.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,192.74,19.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,221.59,24.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,231.81,19.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,237.93,16.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,242.82,19.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="-82.519997" y="27.450001"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-89.519997" y="29.98"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,161.55,-5.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,175.24,-10.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,193.4,-5.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,199.22,-10.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,207.48,-5.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,219.52,-10.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,236.98,-5.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,241.87,-10.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,250.12,-5.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,260.33,-10.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="204.42" y="-16.860001"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="208.5835" y="-16.860001"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="214.83499" y="-16.860001"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="217.96075" y="-16.860001"> 8.</T.S.pan> <tspan style="font-size: 12.50px; " x="224.21225" y="-16.860001"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="-63.389999" y="25.23"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-69.316422" y="25.23"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,197.12,-30.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,206.42,-35.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="258.32999" y="0.62"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="262.4935" y="0.62"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="268.745" y="0.62"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="271.87076" y="0.62"> 9.</T.S.pan> <tspan style="font-size: 12.50px; " x="278.12225" y="0.62"> ）</T.S.pan> </text> </g> </g> </svg></span>他们暗示<S.。pan class="equation" id="EEq36"> <svg height="30.700001" id="M183" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7)"> <g transform="translate(72,-47.44)"> <text transform="matrix(1,0,0,-1,175.68,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̈</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.3140149" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,176.24,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,185.54,56.25)"> <tspan style="font-size: 12.50px; " x="21.799999" y="-7.25"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> </text> <g> <path d="m 207.34,59.37 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,207.34,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="7.4400001" y="-8.7600002"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,223.04,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,233.26,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,239.37,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,244.26,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="214.23" y="-0.34999999"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="218.39349" y="-0.34999999"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="224.645" y="-0.34999999"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="227.77075" y="-0.34999999"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="234.02225" y="-0.34999999"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="240.27374" y="-0.34999999"> ）</T.S.pan> </text> </g> </g> </svg></span>在三维符号中，等式（<a href="#EEq32">3.8</a>）读<S.。pan class="equation" id="EEq37"> <svg height="48.6875" id="M184" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.6875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.6875)"> <g transform="translate(72,-33.05)"> <text transform="matrix(1,0,0,-1,114.35,63.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-7" y="2.54"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,115.6,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,128.32,60.76)"> <tspan style="font-size: 12.50px; " x="83.690002" y="-2.8199999"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="77.690002" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="22.680443" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="39.346943" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="46.298611" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="52.55011" y="0"> 那</T.S.pan> </text> <text transform="matrix(1,0,0,-1,212.26,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,220.61,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,247.33,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,252.2,60.76)"> <tspan style="font-size: 12.50px; " x="-79.07" y="21.08"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="26.618887" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="38.421719" y="0"> ×</T.S.pan> <tspan style="font-size: 12.50px; " x="49.199306" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="56.150974" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="-88.699997" y="23.91"> </T.S.pan> <tspan style="font-size: 12.50px; " x="-72.721169" y="23.91"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="-60.693279" y="23.91"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,197.63,41.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,202.51,36.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,208.76,42.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,216.41,36.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,236,41.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,245.25,36.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="213.24001" y="-12.55"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="217.4035" y="-12.55"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="223.655" y="-12.55"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="226.78075" y="-12.55"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="233.03224" y="-12.55"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="239.28375" y="-12.55"> ）</T.S.pan> </text> </g> </g> </svg></span></span></p> <p><span class="statement" id="head3"><span class="statement-title"><i class="statement-title">相对主义的不变性</i></span><br>而规范动量<S.。vg height="11.2" id="M185" style="vertical-align:-0.11285pt;width:16px;" version="1.1" viewbox="0 0 16 11.2" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2)"> <g transform="translate(72,-63.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>是由<S.。vg height="13.9125" id="M186" style="vertical-align:-2.29482pt;width:15.05px;" version="1.1" viewbox="0 0 15.05 13.9125" width="15.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9125)"> <g transform="translate(72,-60.87)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.84,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>，机械动量，根据(<a href="#EEq32">3.7</a>)，与转换为的变量一致<S.。vg height="10.475" id="M187" style="vertical-align:-0.0pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</T.S.pan> </text> </g> </g> </svg>-量子理论中的矩阵，<S.。vg height="16.674999" id="M188" style="vertical-align:-2.21957pt;width:53.575001px;" version="1.1" viewbox="0 0 53.575001 16.674999" width="53.575001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.675)"> <g transform="translate(72,-58.66)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="24.305832" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-39.39,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>．由于限制(<a href="#EEq22">2.13</a>），（<a href="#EEq22">2.14</a>），<S.。vg height="14.0875" id="M189" style="vertical-align:-0.15048pt;width:23.200001px;" version="1.1" viewbox="0 0 23.200001 14.0875" width="23.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0875)"> <g transform="translate(72,-60.73)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> </g> </g> </svg>遵循<S.。vg height="16.75" id="M190" style="vertical-align:-2.21957pt;width:109.1125px;" version="1.1" viewbox="0 0 109.1125 16.75" width="109.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.75)"> <g transform="translate(72,-58.6)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-59.53,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-49.33,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-38.25,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-33.38,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-29.21,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-20.87,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> 4.</T.S.pan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> </T.S.pan> </text> </g> </g> </svg>，这是比喻的<S.。vg height="16.637501" id="M191" style="vertical-align:-2.29482pt;width:74.5px;" version="1.1" viewbox="0 0 74.5 16.637501" width="74.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.84,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-57.49,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-28.01,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-23.14,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-17.32,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> </g> </g> </svg>无自旋粒子的。因此,<S.。vg height="15.8875" id="M192" style="vertical-align:-2.21957pt;width:28.049999px;" version="1.1" viewbox="0 0 28.049999 15.8875" width="28.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.8875)"> <g transform="translate(72,-59.29)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-61.85,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</T.S.pan> </text> </g> </g> </svg>不能超过光速，<S.。vg height="16.75" id="M193" style="vertical-align:-2.21957pt;width:342px;" version="1.1" viewbox="0 0 342 16.75" width="342" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.75)"> <g transform="translate(72,-58.6)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.815095" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-54.26,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-51.04,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.12743" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="14.040869" y="0"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-32.83,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-24.49,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-6.63,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-1.76,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="10.465011" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,9.28,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,12.5,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="9.7773457" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,22.85,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,27.73,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,31.89,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,40.24,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,58.09,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,62.96,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="32.857883" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,103.43,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,108.3,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,112.47,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,117.34,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4.</T.S.pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="15.50372" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,148.74,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,157.99,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,162.15,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,167.02,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> <</T.S.pan> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,196.68,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> </g> </g> </svg>．方程(<a href="#EEq36">3.10</a>），（<a href="#EEq37">3．11</a>）意味着两者<S.。vg height="11.2" id="M194" style="vertical-align:-0.11285pt;width:16px;" version="1.1" viewbox="0 0 16 11.2" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2)"> <g transform="translate(72,-63.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>-粒子和变量<S.。vg height="10.925" id="M195" style="vertical-align:-0.1881pt;width:15.75px;" version="1.1" viewbox="0 0 15.75 10.925" width="15.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="15.4875" id="M196" style="vertical-align:-1.20384pt;width:14.0375px;" version="1.1" viewbox="0 0 14.0375 15.4875" width="14.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4875)"> <g transform="translate(72,-59.61)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>体验<i>zitterbewung</i>不相互影响的理论。</S.。pan></p> <p><span class="statement" id="head4"><span class="statement-title"><i class="statement-title">充电中心休息框架</i></span><br>确定变量<S.。vg height="11.2" id="M197" style="vertical-align:-0.11285pt;width:16px;" version="1.1" viewbox="0 0 16 11.2" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2)"> <g transform="translate(72,-63.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>根据指控位置，(<a href="#EEq32">3.7</a>)意味着静止系具有这些条件的特征<S.。pan class="equation" id="EEq39"> <svg height="18.799999" id="M198" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.799999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.8)"> <g transform="translate(72,-56.96)"> <text transform="matrix(1,0,0,-1,148.15,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,156.4,65.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,169.12,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> C</T.S.pan> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> O.</T.S.pan> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> N</T.S.pan> <tspan style="font-size: 12.50px; " x="30.094721" y="0"> S.</T.S.pan> <tspan style="font-size: 12.50px; " x="34.870869" y="0"> T.</T.S.pan> <tspan style="font-size: 12.50px; " x="38.346703" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="63.465229" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,238.84,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,247.19,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="211.3" y="-0.58999997"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="215.4635" y="-0.58999997"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="221.715" y="-0.58999997"> ．</T.S.pan> <tspan style="font-size: 12.50px; " x="224.84074" y="-0.58999997"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="231.09225" y="-0.58999997"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="237.34375" y="-0.58999997"> ）</T.S.pan> </text> </g> </g> </svg></span>根据(<a href="#EEq39">3.12</a>），（<a href="#EEq21">2.12</a>),只有<S.。vg height="10.925" id="M199" style="vertical-align:-0.1881pt;width:15.75px;" version="1.1" viewbox="0 0 15.75 10.925" width="15.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>存在于非相对论极限中。</S.。pan></p> <p><span class="statement" id="head5"><span class="statement-title"><i class="statement-title">摆脱抖动bewegung的变量</i></span><br>量(质心坐标[<a href="#B5">7.</a>])<S.。vg height="17.775" id="M200" style="vertical-align:-3.21404pt;width:149.89999px;" version="1.1" viewbox="0 0 149.89999 17.775" width="149.89999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.775)"> <g transform="translate(72,-57.78)"> <text transform="matrix(1,0,0,-1,-65.27,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.6766019" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.77,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-36.86,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-28.25,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="15.50372" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="25.231054" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="31.482553" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,9.35,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,14.22,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,26.64,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,36.86,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,42.97,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>遵循<S.。vg height="16.637501" id="M201" style="vertical-align:-2.29482pt;width:123.9625px;" version="1.1" viewbox="0 0 123.9625 16.637501" width="123.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-65.64,63.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="0.37" y="2.3499999"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.306602" y="2.3499999"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,67.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.77,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="24.755939" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="33.633072" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="38.821815" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="46.06105" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="49.536884" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="55.788387" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,6.14,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,11.01,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,21.29,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>，所以，它有自由动态<S.。vg height="13.5875" id="M202" style="vertical-align:-0.17555pt;width:43.212502px;" version="1.1" viewbox="0 0 43.212502 13.5875" width="43.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5875)"> <g transform="translate(72,-61.13)"> <text transform="matrix(1,0,0,-1,-65.64,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̈</T.S.pan> <tspan style="font-size: 12.50px; " x="0.37" y="2.3499999"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.306602" y="2.3499999"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-55.77,61.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>．还请注意,<S.。vg height="13.9125" id="M203" style="vertical-align:-2.29482pt;width:15.05px;" version="1.1" viewbox="0 0 15.05 13.9125" width="15.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9125)"> <g transform="translate(72,-60.87)"> <text transform="matrix(1,0,0,-1,-71.95,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.84,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>代表机械动量<S.。vg height="11.2" id="M204" style="vertical-align:-0.17555pt;width:16px;" version="1.1" viewbox="0 0 16 11.2" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2)"> <g transform="translate(72,-63.04)"> <text transform="matrix(1,0,0,-1,-65.27,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̃</T.S.pan> <tspan style="font-size: 12.50px; " x="-6.6766019" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.07,68.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>-粒子。<br>作为经典的四维自旋向量，我们取<S.。vg height="19.5875" id="M205" style="vertical-align:-4.74141pt;width:105.5375px;" version="1.1" viewbox="0 0 105.5375 19.5875" width="105.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.5875)"> <g transform="translate(72,-56.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-53.65,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-35.73,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="9.7147198" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="14.650848" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-15.69,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-9.58,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-4.69,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,2.07,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> </T.S.pan> </text> </g> </g> </svg>．在自由理论中没有旋进，<S.。vg height="13.475" id="M206" style="vertical-align:-0.17555pt;width:45.862499px;" version="1.1" viewbox="0 0 45.862499 13.475" width="45.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.475)"> <g transform="translate(72,-61.22)"> <text transform="matrix(1,0,0,-1,-64.57,64.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</T.S.pan> <tspan style="font-size: 12.50px; " x="-7.3800001" y="2.72"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-62.95,66.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-53.65,61.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>．在休息框架中，它减少到<S.。vg height="14.525" id="M207" style="vertical-align:-0.23827pt;width:42.112499px;" version="1.1" viewbox="0 0 42.112499 14.525" width="42.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.525)"> <g transform="translate(72,-60.38)"> <text transform="matrix(1,0,0,-1,-71.95,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-56.65,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>那<S.。vg height="14.1375" id="M208" style="vertical-align:-2.5707pt;width:69.474998px;" version="1.1" viewbox="0 0 69.474998 14.1375" width="69.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1375)"> <g transform="translate(72,-60.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="22.455387" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="32.18272" y="0"> ×</T.S.pan> <tspan style="font-size: 12.50px; " x="42.960308" y="0"> </T.S.pan> </text> </g> </g> </svg>．</S.。pan></p> <p><span class="statement" id="head6"><span class="statement-title"><i class="statement-title">与Barut-Zanghi (BZ)模型的比较</i></span><br>BZ旋转粒子[<a href="#B13">16</a>]广泛使用[<a href="#B20">19</a>-<a href="#B25">24</a>]用于自旋效应的半经典分析。从偶数变量开始<S.。vg height="11.175" id="M209" style="vertical-align:-3.22282pt;width:14.7125px;" version="1.1" viewbox="0 0 14.7125 11.175" width="14.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.175)"> <g transform="translate(72,-63.06)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-65.71,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>,在那里<S.。vg height="12.8875" id="M210" style="vertical-align:-1.76814pt;width:79.125px;" version="1.1" viewbox="0 0 79.125 12.8875" width="79.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="28.806911" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="34.020664" y="0"> 2</T.S.pan> <tspan style="font-size: 12.50px; " x="40.272163" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="45.473412" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="51.724911" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="56.938663" y="0"> 4.</T.S.pan> </text> </g> </g> </svg>是<S.。vg height="13.45" id="M211" style="vertical-align:-2.21957pt;width:52.650002px;" version="1.1" viewbox="0 0 52.650002 13.45" width="52.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> S.</T.S.pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> O.</T.S.pan> <tspan style="font-size: 12.50px; " x="15.978834" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="26.393833" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="31.595081" y="0"> 3.</T.S.pan> <tspan style="font-size: 12.50px; " x="37.846581" y="0"> ）</T.S.pan> </text> </g> </g> </svg>-旋量指数，Barut和Zanghi根据<S.。vg height="18.225" id="M212" style="vertical-align:-4.74141pt;width:114.0125px;" version="1.1" viewbox="0 0 114.0125 18.225" width="114.0125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.225)"> <g transform="translate(72,-57.42)"> <text transform="matrix(1,0,0,-1,-71.95,62.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.82,59.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-50.13,62.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 1</T.S.pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> 4.</T.S.pan> <tspan style="font-size: 12.50px; " x="32.170219" y="0"> ）</T.S.pan> <tspan style="font-size: 12.50px; " x="36.333717" y="0"> </T.S.pan> </text> <g> <path d="m -9.9,70.71 6.24,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-9.9,62.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="6.238997" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,2.69,59.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,12.92,62.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>．我们指出(<a href="#EEq32">3.7</a>） - （<a href="#EEq32">3.9</a>)，与bz模型吻合，识别<S.。vg height="14.0875" id="M213" style="vertical-align:-0.15048pt;width:61.537498px;" version="1.1" viewbox="0 0 61.537498 14.0875" width="61.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0875)"> <g transform="translate(72,-60.73)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-50.02,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ↔</T.S.pan> <tspan style="font-size: 12.50px; " x="15.041109" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-28.64,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> </g> </g> </svg>那<S.。vg height="11.525" id="M214" style="vertical-align:-0.15048pt;width:70.400002px;" version="1.1" viewbox="0 0 70.400002 11.525" width="70.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.525)"> <g transform="translate(72,-62.78)"> <text transform="matrix(1,0,0,-1,-71.95,62.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-63.7,67.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.329968" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-50,62.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ↔</T.S.pan> <tspan style="font-size: 12.50px; " x="15.041109" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-25.95,68.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> <tspan style="font-size: 8.75px; " x="5.3212161" y="0"> </T.S.pan> </text> </g> </g> </svg>．此外，我们的模型包含了这些方程<S.。vg height="19.887501" id="M215" style="vertical-align:-4.74141pt;width:225.1125px;" version="1.1" viewbox="0 0 225.1125 19.887501" width="225.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8875)"> <g transform="translate(72,-56.09)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</T.S.pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-59.53,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-49.33,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</T.S.pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,-38.25,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-33.38,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-29.21,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</T.S.pan> </text> <text transform="matrix(1,0,0,-1,-20.87,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</T.S.pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> 4.</T.S.pan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="36.096161" y="0"> 那</T.S.pan> <tspan style="font-size: 12.50px; " x="41.309914" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,26.56,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,32.39,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,40.64,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5.</T.S.pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </T.S.pan> </text> <text transform="matrix(1,0,0,-1,53.63,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</T.S.pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="20.204847" y="0"> </T.S.pan> <tspan style="font-size: 12.50px; " x="25.393593" y="0"> ℏ</T.S.pan> <tspan style="font-size: 12.50px; " x="36.108665" y="0"> =</T.S.pan> <tspan style="font-size: 12.50px; " x="48.149052" y="0"> 0.</T.S.pan> </text> </g> </g> </svg>．第一个方程保证电荷中心不超过光速。第二个方程隐含狄拉克方程。(在BZ理论中[<a href="#B13">16</a>]，纺丝颗粒的质量不是从模型固定的。）</S.。pan></p> <h4 id="acknowledgment">承认</h4> <p>这项工作得到了巴西FAPEMIG基金会的支持。</p> </div> <div class="xml-content"> <h4 class="references" id="references">参考文献</h4> <ol> <li id="B1a">A. 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height="24"><span class="text">引用</S.。pan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-cHSUfg kdoIIa article_bottom_toolbar"> <div class="sc-cTjmhe begQDP accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-eAKXzc bESoPs" title="" role="presentation" 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height="24"><span class="sc-gbOuXE SDMqt">下载其他格式</S.。pan><span class="sc-dRFtgE jooXYL">更多的</S.。pan></span> <span class="sc-htoDjs bMdQcY sc-bfYoXt VdeWO icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-cugefK dCMfhd"> <a class="sc-htpNat bUhGXt link sc-fnwBNb kfscSt open_panel" href="//www.newsama.com/downloads/journals/amp/2011/680367.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-iNhVCk brvugV"> epub.</div><img alt="" class="sc-EHOje jOLhQl sc-eAKXzc bESoPs" title="" role="presentation" 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height="24"><span class="sc-gbOuXE SDMqt">订单印刷副本</S.。pan><span class="sc-dRFtgE jooXYL">订单</S.。pan></span><span class="sc-htoDjs kNoiZu sc-bfYoXt VdeWO right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-cqpYsc krPIEq"> <div class="sc-hBbWxd hdkxPJ"> <div> 的观点<S.。pan>1035.</S.。pan> </div> <div> 下载<S.。pan>749.</S.。pan> </div> </div> <div> <div class="sc-dyGzUR cmbuIE"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2011/680367" data-style="small_circle"></span>引用</div> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-gkFcWv gXvjfo" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享帖子</h3> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2011/680367&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" role="presentation" 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