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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 173, Number 3, Pages 375–391
DOI: https://doi.org/10.4213/tmf8319
(Mi tmf8319)
 

This article is cited in 23 scientific papers (total in 23 papers)

Integrating Klein–Gordon–Fock equations in an external electromagnetic field on Lie groups

A. A. Magazev

Omsk State Technical University, Omsk, Russia
References:
Abstract: We investigate the structure of the Klein–Gordon–Fock equation symmetry algebra on pseudo-Riemannian manifolds with motions in the presence of an external electromagnetic field. We show that in the case of an invariant electromagnetic field tensor, this algebra is a one-dimensional central extension of the Lie algebra of the group of motions. Based on the coadjoint orbit method and harmonic analysis on Lie groups, we propose a method for integrating the Klein–Gordon–Fock equation in an external field on manifolds with simply transitive group actions. We consider a nontrivial example on the four-dimensional group $E(2)\times\mathbb{R}$ in detail.
Keywords: Klein–Gordon–Fock equation, symmetry operator, Lie group, Lie algebra, $\lambda $-representation.
Received: 15.12.2011
Revised: 22.05.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 3, Pages 1654–1667
DOI: https://doi.org/10.1007/s11232-012-0139-x
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Magazev, “Integrating Klein–Gordon–Fock equations in an external electromagnetic field on Lie groups”, TMF, 173:3 (2012), 375–391; Theoret. and Math. Phys., 173:3 (2012), 1654–1667
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8319
  • https://www.mathnet.ru/eng/tmf/v173/i3/p375
  • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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