Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups

A. I. Breev, E. A. Mosman

Research output: Contribution to journalArticle

Abstract

The algebra of first-order symmetry operators of the Dirac equation on four-dimensional Lie groups with right-invariant metric is investigated. It is shown that the algebra of symmetry operators is in general not a Lie algebra. Noncommutative reduction mediated by spin symmetry operators is investigated. For the Dirac equation on the Lie group SO(2,1) a parametric family of particular solutions obtained by the method of noncommutative integration over a subalgebra containing a spin symmetry operator is constructed.

Original languageEnglish
Pages (from-to)1153-1163
Number of pages11
JournalRussian Physics Journal
Volume59
Issue number8
DOIs
Publication statusPublished - 1 Dec 2016

Keywords

  • Dirac equation
  • noncommutative integration
  • symmetry algebra

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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