{
  "id": "2205.11254",
  "version": "v1",
  "published": "2022-05-19T17:22:54.000Z",
  "updated": "2022-05-19T17:22:54.000Z",
  "title": "Quantum models a la Gabor for space-time metric",
  "authors": [
    "Gilles Cohen-Tannoudji",
    "Jean-Pierre Gazeau",
    "Célestin Habonimana",
    "Juma Shabani"
  ],
  "comment": "21 pages",
  "categories": [
    "quant-ph",
    "gr-qc",
    "math-ph",
    "math.MP"
  ],
  "abstract": "As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space $\\left(x,k\\right)$ into Hilbertian operators. The $x=\\left(x^{\\mu}\\right)$'s are space-time variables and the $k=\\left(k^{\\mu}\\right)$'s are their conjugate wave vector-frequency variables. The procedure is first applied to the variables $\\left(x,k\\right)$ and produces canonically conjugate essentially self-adjoint operators. It is next applied to the metric field $g_{\\mu\\nu}(x)$ of general relativity and yields regularised semi-classical phase space portraits $\\check{g}_{\\mu\\nu}(x)$. The latter give rise to modified tensor energy density. Examples are given with the uniformly accelerated reference system and the Schwarzschild metric. Interesting probabilistic aspects are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-19T17:22:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L65",
      "81S05",
      "81S30",
      "83C45",
      "81R30"
    ],
    "keywords": [
      "quantum models",
      "space-time metric",
      "semi-classical phase space portraits",
      "conjugate essentially self-adjoint operators",
      "regularised semi-classical phase space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}