Geodesic
Integrating Klein--Gordon--Fock equations in an~external electromagnetic field on Lie groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 375-391

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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 algebra, $\lambda $-representation.
Mots-clés : Lie group 
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     author = {A. A. Magazev},
     title = {Integrating {Klein--Gordon--Fock} equations in an~external electromagnetic field on {Lie} groups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {375--391},
     publisher = {mathdoc},
     volume = {173},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a2/}
}
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A. A. Magazev. Integrating Klein--Gordon--Fock equations in an~external electromagnetic field on Lie groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 375-391. http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a2/