On a noncontractible family of representations of the canonical commutation relations
In this paper, the authors construct an explicit family of irreducible representations of the canonical commutation relations parametrised by the space of pairs of transverse Lagrangian subspaces in the complexification of a symplectic vector space. In particular, a non-contractible family of representations, constructed by Lion-Vergne and parametrised by the space of pairs of transverse real Lagrangian subspaces, is extended to a family parametrised by space of pairs of transverse complex Lagrangian subspaces. For some representations, the operators can be exponentiated to obtain unitary representations of the canonical and Weyl commutation relations, and this allows the reconstruction of previously studied contractible families of representations.
scientific article; zbMATH DE number 7396049
scientific article