2021/12/31 by V. V. Obukhov · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:83C10 #msc:83C15 #msc:83C20 #msc:83C50
paper · pdf · doi:10.1063/5.0080703
published as Journal of Mathematical Physics. Vol.63, Issue 2, 2022 · 26 pages, submitted to Journal of Mathematical Physics
arxiv created 2022/01/27 · arxiv updated 2022/02/22
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.