The metaplectic correction in geometric quantization

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• 作者：Gijs M. Tuynman ^{Gijs.Tuynman@univ-lille1.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53D50 ; 81S10
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：106
• 期：Complete
• 页码：401-426
• 全文大小：575 K

文摘

Let formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044016300936&_mathId=si1.gif&_user=111111111&_pii=S0393044016300936&_rdoc=1&_issn=03930440&md5=b985dd849efbdc014336d6b58ae9be96" title="Click to view the MathML source">P$P$ be a polarization on a symplectic manifold for which there exists a metalinear frame bundle. We show that for any other compatible polarization formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044016300936&_mathId=si2.gif&_user=111111111&_pii=S0393044016300936&_rdoc=1&_issn=03930440&md5=6511ffd8e1fd40d183dd4d53894c9865" title="Click to view the MathML source">P^′$P^{\prime }$ there exists a unique metalinear frame bundle such that the BKS-pairing is well defined. This means that we do not need the metaplectic frame bundle (nor a positivity condition on formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0393044016300936&_mathId=si1.gif&_user=111111111&_pii=S0393044016300936&_rdoc=1&_issn=03930440&md5=b985dd849efbdc014336d6b58ae9be96" title="Click to view the MathML source">P$P$) to achieve this goal, and thus the name “metalinear correction” would be more appropriate than the commonly used name “metaplectic correction”.