Covariant representations in a fibre bundle framework
type: Item
instance of: scholarly article
title: Covariant representations in a fibre bundle framework
zbMATH Open document ID: 0616.22009
DOI: 10.1016/0034-4877(85)90040-0
author: Manuel Asorey
author: L. J. Boya
author: J. F. Cariñena
published in: Reports on Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: Two kinds or representations of an analytic semidirect product G of a Lie group K by an abelian Lie kernel N are studied in the present paper within a unifying fibre bundle approach. These are the representations induced (in Mackey's sense) by strongly continuous unitary representations of the isotropy group \(G_{\chi_ 0}\) of a character \(\chi_ 0\) of N (the canonical representations of G) and those induced by representations of K (the covariant representations of G). A relationship between both types of representations is established which allows a selection of irreducible covariant representations in two different ways. This result is then applied to the Poincaré group.
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 22D30
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 55R10
zbMATH DE Number: 3998111
zbMATH Keywords: gauge transformations
zbMATH Keywords: induced representation
zbMATH Keywords: analytic semidirect product
zbMATH Keywords: fibre bundle
zbMATH Keywords: canonical representations
zbMATH Keywords: irreducible covariant representations
zbMATH Keywords: Poincaré group
Wikidata QID: Q62561044
MaRDI profile type: Publication
full work available at URL: 0034-4877(85)90040-0
OpenAlex ID: W2054018094
cites work: On unitary ray representations of continuous groups
cites work: Splitting and representation groups for Polish groups
cites work: Semiunitary projective representations of the complete Galilei group
cites work: Unitary representations of group extensions. I
cites work: Lie groups and quantum mechanics
cites work: General theory of covariant particle equations
cites work: Q5825483
cites work: Fibre bundles associated with space-time
cites work: Dilatations and the Poincaré group
cites work: Locally-operating realizations of groups and superequivalence of factor systems
cites work: Galilean relativistic wave equations
cites work: Vector bundle representations of groups in quantum physics
cites work: Q5537296
cites work: On the continuity of the boosts for each orbit
cites work: Poincaré Group and the Invariant Relativistic Equations for Massive Particles of Any Spin
description: scientific article; zbMATH DE number 3998111