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

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.

16 pages

Cited by in corpus (8)

• Maxwell's equations in homogeneous spaces for admissible electromagnetic fields
• Algebra of the symmetry operators of the Klein-Gordon-Fock equation for the case when groups of motions $G_3$ act transitively on null subsurfaces of spacetime
• Algebras of integrals of motion for the Hamilton-Jacobi and Klein-Gordon-Fock equations in spacetime with a four-parameter groups of motions in the presence of an external electromagnetic field
• Maxwell equations in homogeneous spaces with solvable groups of motions
• Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions
• Classification of the non-null electrovacuum solution of Einstein-Maxwell equations with three-parameter abelian group of motions
• Classification of Petrov Homogeneous Spaces
• Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions