{
  "id": "1501.03750",
  "version": "v1",
  "published": "2015-01-15T17:33:55.000Z",
  "updated": "2015-01-15T17:33:55.000Z",
  "title": "The quantum Cauchy functional and space-time approach to relativistic quantum mechanics",
  "authors": [
    "A. A. Beilinson"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We show that the quantum complex Cauchy functional on bump functions (see \\cite{16}), yields a generalized complex Cauchy process, which is a generalized functional on the bump functionals on Borel cylindrical sets of a real Hilbert space, whose support is locally compact for the uniform convergence topology with derivatives in $L_2 (0,t)$. The retarded Green's functions of the Dirac electron and Einstein photon viewed as complex matrix-vaued functionals on bump functionals, also yield generalized complex matrix-valued processes of Cauchy-Dirac and Cauchy-Maxwell, which are generalized functional on the bump functionals on Borel cylindrical sets of a real Hilbert space, but their supports are compact for the uniform convergence topology with derivatives in $L_2 (0,t)$. We study the way the classical relativistic mechanics of particle comes from the quantum mechanics of the free Dirac particle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-15T17:33:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relativistic quantum mechanics",
      "quantum cauchy functional",
      "space-time approach",
      "generalized complex matrix-valued processes",
      "real hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150103750B"
    }
  }
}