## 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:nbn:de:hbz:386-kluedo-11066 Preprint English 1997 1997 Technische Universität Kaiserslautern 2000/09/25 Fachbereich Physik 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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