2022/01/25 by V. V. Obukhov · 1 citation
Physics and Astronomy · Mathematics · #gr-qc #math-ph #math.MP #msc:83C10 #msc:83C15 #msc:83C20 #msc:83C50
paper · pdf · doi:10.3390/sym14020346
published as Symmetry. 2022, 14, 346 · 22 pages. Submitted to Symmetry
arxiv created 2022/01/25 · arxiv updated 2022/02/22
The algebras of the symmetry operators for the Hamilton-Jacobi and Klein-Gordon-Fock equations are found for a charged test particle moving in an external electromagnetic field in a spacetime manifold, on the isotropic (null) hypersurface of which a three-parameter groups of motions act transitively.on the isotropic (null) hypersurface of which a three-parameter groups of motions act transitively. We have found all admissible electromagnetic fields for which such algebras exist. We have proved that an admissible field does not deform the algebra of symmetry operators for the free Hamilton-Jacobi and Klein-Gordon-Fock equations. The results complete the classification of admissible electromagnetic fields in which the Hamilton-Jacobi and Klein-Gordon-Fock equations admit algebras of motion integrals that are isomorphic to the algebras of operators of r-parametric groups of motions of spacetime manifolds if (r ≤ 4).