{
  "id": "1406.5698",
  "version": "v1",
  "published": "2014-06-22T10:39:36.000Z",
  "updated": "2014-06-22T10:39:36.000Z",
  "title": "Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups",
  "authors": [
    "Alexey A. Magazev"
  ],
  "comment": "16 pages",
  "journal": "Theoretical and Mathematical Physics, December 2012, Volume 173, Issue 3, pp 1654-1667",
  "doi": "10.1007/s11232-012-0139-x",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the structure of the Klein-Gordon-Fock equation symmetry algebra on pseudo-Riemannian manifolds with motions in the presence of an external electromagnetic field. We show that in the case of an invariant electromagnetic field tensor, this algebra is a one-dimensional central extension of the Lie algebra of the group of motions. Based on the coadjoint orbit method and harmonic analysis on Lie groups, we propose a method for integrating the Klein-Gordon-Fock equation in an external field on manifolds with simply transitive group actions. We consider a nontrivial example on the four-dimensional group $E(2) \\times \\mathbb{R}$ in detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-22T10:39:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "external electromagnetic field",
      "integrating klein-gordon-fock equations",
      "lie groups",
      "klein-gordon-fock equation symmetry algebra",
      "invariant electromagnetic field tensor"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Theoretical and Mathematical Physics",
      "year": 2012,
      "month": "Dec",
      "volume": 173,
      "number": 3,
      "pages": 1654
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1216159,
      "adsabs": "2012TMP...173.1654M"
    }
  }
}