Functional Representations for Fock Superalgebras
1998 ◽
Vol 01
(02)
◽
pp. 285-324
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Keyword(s):
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 super-analogs 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.
2019 ◽
Vol 31
(08)
◽
pp. 1950026
◽
Keyword(s):
2018 ◽
Vol 21
(01)
◽
pp. 1850002
Keyword(s):