On observable algebras of a class of associative mechanical systems
type: Item
instance of: scholarly article
title: On observable algebras of a class of associative mechanical systems
zbMATH Open document ID: 0584.17012
DOI: 10.1007/BF01017899
author: G. K. Tolokonnikov
published in: Theoretical and Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: It is assumed that the observables of a physical system are the elements of the universal covering \(U(\mathfrak g)\) (or its factor algebra) of some Lie algebra \(\mathfrak g\), and the universal covering \(U(\mathfrak g)\) is assumed to be invariant with respect to the adjoint representation of the Lie group \(G\), for which \(\mathfrak g\) is the Lie algebra. In the first part of the paper a classification is made of the associative algebras of functions that are invariant with respect to the adjoint representation of \(G\), where \(G\) is the group of affine transformations of the real line. The second part of the paper is devoted to the application of the obtained classification to the problem of describing the possible associative Hamiltonian mechanical systems.
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 81Q99
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 3935273
zbMATH Keywords: nonrelativistic quantum mechanics
zbMATH Keywords: algebras of observables
zbMATH Keywords: universal covering
zbMATH Keywords: associative Hamiltonian mechanical systems
reviewed by: Wawrzyniec Guz
MaRDI profile type: Publication
cites work: Q3924413
cites work: Q4115279
cites work: Q5732721
full work available at URL: https://doi.org/10.1007/bf01017899
OpenAlex ID: W1967864043
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description: scientific article; zbMATH DE number 3935273