On Quasifree Representations of Infinite Dimensional Symplectic Group

2002/04/18 by Taku Matsui, Matsui, Taku, Yoshihito Shimada +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0204039

arxiv created 2002/04/18 · arxiv updated 2009/11/30

Abstract

We consider an infinite dimensional generalization of Metaplectic representations (Weil representations) for the (double covering of) symplectic group. Given quasifree states of an infinite dimensional CCR algebra, projective unitary representations of the infinite dimensional symplectic group are constructed via unitary implementors of Bogoliubov automorphisms. Complete classification of these representations up to quasi-equivalence is obtained.

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