On a noncontractible family of representations of the canonical commutation relations
type: Item
instance of: scholarly article
title: On a noncontractible family of representations of the canonical commutation relations
zbMATH Open document ID: 1483.22005
author: Hyunmoon Kim
published in: Journal of Geometry and Physics
publication date: 2021-09-16T00:00:00Z
review text: 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.
reviewed by: Carlos A. M. André
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 81R05
zbMATH DE Number: 7396049
zbMATH Keywords: Heisenberg Lie algebra
zbMATH Keywords: symplectic matrices
zbMATH Keywords: unitary representations
MaRDI profile type: Publication
full work available at URL: j.geomphys.2021.104343
OpenAlex ID: W3188117579
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DOI: 10.1016/J.GEOMPHYS.2021.104343
description: scientific article; zbMATH DE number 7396049