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

Abstract

The algebras of the integrals of motion of the Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle moving in an external electromagnetic field in a spacetime manifold are found. The manifold admits a four-parameter groups of motions that act nontransitively on the spacetime. All admissible electromagnetic fields for which such algebras exist are found. In the case of an arbitrary n-dimensional Riemannian space on which the group of motions acts, it is proved that the admissible field does not deform the algebra of symmetry operators of the free Hamilton-Jacobi and Klein-Gordon-Fock equations. In addition, the system of differential equations, which must be satisfied by the potentials of the admissible electromagnetic field, have been investigated for compatibility.

26 pages, submitted to Journal of Mathematical Physics

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• Maxwell's equations in homogeneous spaces for admissible electromagnetic fields
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• Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions
• Deviation of geodesics and particle trajectories in a gravitational wave of the Bianchi type VI universe
• Gravitational Waves of Type III Shapovalov Spacetimes: Particle Trajectories, Geodesic Deviation and Tidal Accelerations
• Classification of the non-null electrovacuum solution of Einstein-Maxwell equations with three-parameter abelian group of motions
• Noether Symmetry Analysis of the Klein--Gordon and Wave Equations in Bianchi I Spacetime
• Gauging the Maxwell extended $\mathcal{G}\mathcal{L}\left(n,\mathbb{R}\right)$ and $\mathcal{SL}\left(n+1,\mathbb{R}\right)$ algebras
• Type I Shapovalov wave spacetimes in the Brans-Dicke scalar-tensor theory of gravity
• Quasiparticle solutions for the nonlocal NLSE with an anti-Hermitian term in semiclassical approximation
• Quadratic theory of gravity with a scalar field and type I Shapovalov wave spacetimes
• Gravitational wave of the Bianchi VII universe: particle trajectories, geodesic deviation and tidal accelerations