Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in the Stackel spaces of type (1.1)

Abstract

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that Hamilton-Jacobi equation and Klein-Gordon-Fock equation for a charged test particle can be integrated by the method of complete separation of variables are found. The separation is carried out using the complete sets of mutually-commuting integrals of motion of type (1.1). Whereby in a privileged coordinate system the given equations turn into parabolic type equations. Hence, these metrics can be used as models for describing plane gravitational waves.

The article will be published in IJGMMP

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Cited by in corpus (8)

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• 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
• 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
• Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions
• Gravitational wave of the Bianchi VII universe: particle trajectories, geodesic deviation and tidal accelerations