Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions

Abstract

Metric components of potentials of admissible electromagnetic fields in spaces with simply transitive four-parameter motion group are found. The components of frame vectors corresponding to the components of the metric tensors found by Petrov are given. The results obtained complement the coordinate-free classification given by Magazev et al. Previously, admissible electromagnetic fields were found for the case when three- and four-parameter groups of motions act on hypersurfaces of spacetime. Thus, non-equivalent sets of potentials for all electromagnetic fields that admit three- and four-parameter groups of motions are known now.