{
  "id": "2112.15138",
  "version": "v2",
  "published": "2021-12-30T17:25:01.000Z",
  "updated": "2022-01-27T18:45:15.000Z",
  "title": "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",
  "authors": [
    "V. V. Obukhov"
  ],
  "comment": "26 pages, submitted to Journal of Mathematical Physics",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-01-27T18:45:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "83C10",
      "83C15",
      "83C20",
      "83C50"
    ],
    "keywords": [
      "external electromagnetic field",
      "klein-gordon-fock equations",
      "four-parameter groups",
      "hamilton-jacobi",
      "admissible electromagnetic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}