{
  "id": "1912.12444",
  "version": "v1",
  "published": "2019-12-28T11:40:13.000Z",
  "updated": "2019-12-28T11:40:13.000Z",
  "title": "Quasiclassical approximation for magnetic monopoles",
  "authors": [
    "Yuri A. Kordyukov",
    "Iskander A. Taimanov"
  ],
  "comment": "17 pages",
  "categories": [
    "math-ph",
    "math.DG",
    "math.MP",
    "math.SP"
  ],
  "abstract": "A quasiclassical approximation is constructed to describe the eigenvalues of the magnetic Laplacian on a compact Riemannian manifold in the case when the magnetic field is not given by an exact 2-form. For this, the multidimensional WKB method in the form of Maslov canonical operator is applied. In this case, the canonical operator takes values in sections of a nontrivial line bundle. The constructed approximation is demonstrated for the Dirac magnetic monopole on the two-dimensional sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-28T11:40:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasiclassical approximation",
      "compact riemannian manifold",
      "dirac magnetic monopole",
      "nontrivial line bundle",
      "multidimensional wkb method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}