Group manifold analysis of the structure of relativistic quantum dynamics
type: Item
instance of: scholarly article
title: Group manifold analysis of the structure of relativistic quantum dynamics
zbMATH Open document ID: 0588.58027
DOI: 10.1016/0003-4916(85)90306-9
published in: Annals of Physics
publication date: 1985-01-01T00:00:00Z
review text: In the paper a group law is given from which a relativistic quantum system with an invariant evolution parameter is obtained, the position operator belonging to the Lie algebra of the group. The motivation of the procedure is exposed in the introduction, mentioning the main difficulties involved. Section 2 presents a brief account of the relativistic quantum dynamics, without the rest mass energy, derived from the pseudoextensions P\({\tilde \otimes}U(1)\) of Poincaré group P by U(1). The breaking of the group structure by the introduction of the rest mass is analyzed. Section 3 gives the group \(G_{15}\) (including P) as a contraction of the conformal group, the additional parameters leading to the covariant position operators. Section 4 applies the quantization formalism to the central extension \(\tilde G_{16}\) of \(G_{15}\) by U(1). Section 5 studies the restriction to the mass shell when the quantization 1-form corresponding to the Klein-Gordon equation may be derived from the quantum group \(\tilde G_{16}\). An action of P is generated defining an orbit in the former group manifold. Section 6 contains final remarks on possible extensions of the work in the spirit of Klein's Erlangen program. An appendix summarizes the main formulae on P used in the text.
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 81Q99
Mathematics Subject Classification ID: 83C40
zbMATH DE Number: 3944894
zbMATH Keywords: relativistic quantum dynamics
author: Víctor Aldaya
author: José A. De Azcárraga
MaRDI profile type: Publication
full work available at URL: 0003-4916(85)90306-9
OpenAlex ID: W1977693334
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description: scientific article; zbMATH DE number 3944894