On Quasifree Representations of Infinite Dimensional Symplectic Group

Details On Quasifree Representations of Infinite Dimensional Symplectic Group On Quasifree Representations of Infinite Dimensional Symplectic Group

2002-04-18

arxiv.org/abs/math-ph/0204039v1

Physics

Mathematical Physics

Scientific paper

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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