The Wigner-Bargmann theorem in the pseudo-unitary case
type: Item
instance of: scholarly article
title: The Wigner-Bargmann theorem in the pseudo-unitary case
zbMATH Open document ID: 0543.47029
DOI: 10.1007/BF02329736
author: N. E. Zubov
published in: Annals of Global Analysis and Geometry
publication date: 1983-01-01T00:00:00Z
review text: Let E be a complex vector space with an indefinite inner product, and \(\tilde E\) the corresponding projective space. The author considers the problem of lifting projective mappings \(T:\tilde E\to \tilde E\) to pseudo-unitary or anti-pseudo-unitary mappings \(U:E\to E.\) He proves that this can be done under natural conditions on T, thereby generalizing the classical result of Wigner for a definite inner product space. Similarly he considers the problem of lifting a projective representation on \(\tilde E\), of a Lie group G, to a pseudo-unitary or anti-pseudo-unitary representation on E. This can be done for a wide class of Lie groups and projective representations in the case that E is a J-space. This generalizes a result of Bargmann and extensions of it by Bracci, Morchie and Strocchi.
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 3863918
zbMATH Keywords: isotropic
zbMATH Keywords: indefinite inner product
zbMATH Keywords: projective space
zbMATH Keywords: lifting projective mappings
zbMATH Keywords: anti-pseudo-unitary mappings
zbMATH Keywords: lifting a projective representation
zbMATH Keywords: anti-pseudo-unitary representation
reviewed by: Alan J. Pryde
MaRDI profile type: Publication
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cites work: Note on Wigner's Theorem on Symmetry Operations
cites work: Q4774569
cites work: Wigner's theorem on symmetries in indefinite metric spaces
cites work: Q3273946
cites work: Lie groups and quantum mechanics
description: scientific article; zbMATH DE number 3863918