Quantum symmetries and the Weyl–Wigner product of group representations

Bracken, A. J., Cassinelli, G. and Wood, J. G. (2003) Quantum symmetries and the Weyl–Wigner product of group representations. Journal of Physics A: Mathematical and General, 36 4: 1033-1056. doi:10.1088/0305-4470/36/4/313

Author Bracken, A. J.
Cassinelli, G.
Wood, J. G.
Title Quantum symmetries and the Weyl–Wigner product of group representations
Journal name Journal of Physics A: Mathematical and General   Check publisher's open access policy
ISSN 0305-4470
Publication date 2003-01-31
Sub-type Article (original research)
DOI 10.1088/0305-4470/36/4/313
Volume 36
Issue 4
Start page 1033
End page 1056
Total pages 24
Editor E. Corrigan
Place of publication United Kingdom
Publisher Institute of Physics Publishing
Language eng
Subject 230103 Rings And Algebras
240402 Quantum Optics and Lasers
01 Mathematical Sciences
Abstract In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.
Keyword Deformation theory
Phase-space methods
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mathematics and Physics
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