On Quasifree Representations of Infinite Dimensional Symplectic Group

TL;DR

This paper extends the concept of Metaplectic representations to infinite dimensions, constructing and classifying quasifree representations of the infinite dimensional symplectic group using CCR algebra automorphisms.

Contribution

It provides a comprehensive classification of quasifree representations of the infinite dimensional symplectic group, generalizing finite-dimensional results.

Findings

Constructed projective unitary representations from quasifree states.

Classified these representations up to quasi-equivalence.

Extended the theory of Metaplectic representations to infinite dimensions.

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.