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)×ℝ in detail.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 173, No. 3, pp. 375–391, December, 2012.
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Magazev, A.A. Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups. Theor Math Phys 173, 1654–1667 (2012). https://doi.org/10.1007/s11232-012-0139-x
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DOI: https://doi.org/10.1007/s11232-012-0139-x