2014/06/22 by Alexey A. Magazev · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP
paper · pdf · doi:10.1007/s11232-012-0139-x
published as Theoretical and Mathematical Physics, December 2012, Volume 173, Issue 3, pp 1654-1667 · 16 pages
arxiv created 2014/06/22 · arxiv updated 2014/06/24
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.