Email this article Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups
- Authors: Breev A.I.1,2, Mosman E.A.1,2
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Affiliations:
- National Research Tomsk State University
- National Research Tomsk Polytechnic University
- Issue: Vol 59, No 8 (2016)
- Pages: 1153-1163
- Section: Article
- URL: https://bakhtiniada.ru/1064-8887/article/view/237473
- DOI: https://doi.org/10.1007/s11182-016-0885-6
- ID: 237473
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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.
About the authors
A. I. Breev
National Research Tomsk State University; National Research Tomsk Polytechnic University
Author for correspondence.
Email: breev@mail.tsu.ru
Russian Federation, Tomsk; Tomsk
E. A. Mosman
National Research Tomsk State University; National Research Tomsk Polytechnic University
Email: breev@mail.tsu.ru
Russian Federation, Tomsk; Tomsk
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