{
  "id": "2009.11334",
  "version": "v1",
  "published": "2020-09-23T18:35:48.000Z",
  "updated": "2020-09-23T18:35:48.000Z",
  "title": "All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations",
  "authors": [
    "Cesar R. de Oliveira",
    "Wagner Monteiro"
  ],
  "comment": "34 pages. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We use boundary triples to find a parametrization of all self-adjoint extensions of the magnetic Schr\\\"odinger operator, in a quasi-convex domain~$\\Omega$ with compact boundary, and magnetic potentials with components in $\\textrm{W}^{1}_{\\infty}(\\overline{\\Omega})$. This gives also a new characterization of all self-adjoint extensions of the Laplacian in nonregular domains. Then we discuss gauge transformations for such self-adjoint extensions and generalize a characterization of the gauge equivalence of the Dirichlet magnetic operator for the Dirichlet Laplacian; the relation to the Aharonov-Bohm effect, including irregular solenoids, is also discussed. In particular, in case of (bounded) quasi-convex domains it is shown that if some extension is unitarily equivalent (through the multiplication by a smooth unit function) to a realization with zero magnetic potential, then the same occurs for all self-adjoint realizations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-23T18:35:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B25",
      "35J10",
      "35J25",
      "35Q40",
      "78A25"
    ],
    "keywords": [
      "self-adjoint extensions",
      "gauge transformations",
      "magnetic laplacian",
      "nonsmooth domains",
      "zero magnetic potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}