The Segal-Shale-Weil representation, the indices of Kashiwara and Maslov, and quantum mechanics

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• 作者：Michael C. Berg ^{mberg@lmu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 05C38 ; 15A15 ; secondary ; 05A15 ; 15A18
• 刊名：Expositiones Mathematicae
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：34
• 期：2
• 页码：145-209
• 全文大小：515 K

文摘

We produce a connection between the Weil 2-cocycles defining the local and adèlic metaplectic groups defined over a global field, i.e. the double covers of the attendant local and adèlic symplectic groups, and local and adèlic Maslov indices of the type considered by Souriau and Leray. With the latter tied to phase integrals occurring in quantum mechanics, we provide a formulation of quadratic reciprocity for the underlying field, first in terms of an adèlic phase integral, and then in terms of generalized time evolution unitary operators.