{
  "id": "2201.12104",
  "version": "v1",
  "published": "2022-01-28T13:23:16.000Z",
  "updated": "2022-01-28T13:23:16.000Z",
  "title": "Global and microlocal aspects of Dirac operators: propagators and Hadamard states",
  "authors": [
    "Matteo Capoferri",
    "Simone Murro"
  ],
  "comment": "40 pages, 2 pictures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy-compact globally hyperbolic 4-manifolds. We realise the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals -- the positive and negative Dirac propagators -- global in space and in time, with distinguished complex-valued geometric phase functions. As applications, we relate the Cauchy evolution operators with the Feynman propagator and construct Cauchy surfaces covariances of quasifree Hadamard states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-28T13:23:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L45",
      "35Q41",
      "58J40",
      "53C50",
      "58J45",
      "81T05"
    ],
    "keywords": [
      "dirac operator",
      "hadamard states",
      "cauchy evolution operator",
      "microlocal aspects",
      "complex-valued geometric phase functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}