{
  "id": "2107.08754",
  "version": "v1",
  "published": "2021-07-19T11:05:08.000Z",
  "updated": "2021-07-19T11:05:08.000Z",
  "title": "Scalar field in $\\mathrm{AdS}_2$ and representations of $\\widetilde{\\mathrm{SL}}(2,\\mathbb{R})$",
  "authors": [
    "Atsushi Higuchi",
    "Lasse Schmieding",
    "David Serrano Blanco"
  ],
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We analyse the solutions of the Klein-Gordon equation in the universal covering space of two-dimensional anti-de Sitter spacetime for different ranges of the mass of the scalar field. For certain values of the mass parameter, we impose a suitable set of boundary conditions which make the spatial component of the Klein-Gordon operator self-adjoint. Finally, we use the transformation properties of the mode solutions under the isometry group of the theory, namely, the universal covering group of $\\mathrm{SL}(2,\\mathbb{R})$, in order to determine which self-adjoint boundary conditions are invariant under the action of this group and which result in positive-frequency solutions forming unitary representations of this group, which are classified in a manner similar to those for $\\mathrm{SL}(2,\\mathbb{R})$ given by Bargmann.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-19T11:05:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81T40",
      "20C35",
      "81Q10"
    ],
    "keywords": [
      "scalar field",
      "positive-frequency solutions forming unitary representations",
      "two-dimensional anti-de sitter spacetime",
      "self-adjoint boundary conditions",
      "klein-gordon operator self-adjoint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}