Functional Representations for Fock Superalgebras

Details Functional Representations for Fock Superalgebras Functional Representations for Fock Superalgebras

1997-08-12

arxiv.org/abs/hep-th/9708069v1

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, Latex

Scientific paper

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 Z2-graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.

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