Functional Representations for Fock Superalgebras

  • The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel - including the Bargmann-Fock representation - and of the Wiener-Segal representation. The latter representation requires the investigation of Wick ordering on Z 2 -graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.

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Author:Joachim Kupsch, Oleg G. Smolyanov
URN (permanent link):urn:nbn:de:hbz:386-kluedo-11066
Document Type:Preprint
Language of publication:English
Year of Completion:1997
Year of Publication:1997
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Physik
DDC-Cassification:530 Physik

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