{
  "id": "1204.1858",
  "version": "v3",
  "published": "2012-04-09T11:35:19.000Z",
  "updated": "2012-06-18T11:20:57.000Z",
  "title": "Classical/Quantum=Commutative/Noncommutative?",
  "authors": [
    "Vladimir V. Kisil"
  ],
  "comment": "8 pages, AMS-LaTeX, no figures. v2: small improvements and additional references; v3: small improvements, additional references, Russian translation is added",
  "journal": "Izvestiya Komi nauchnogo centra UrO RAN, v. 3(11), p. 4-9, 2012",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.HO",
    "math.MP"
  ],
  "abstract": "In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires noncommutative one (q-numbers). The rest of theory can be unchanged. In this paper we critically review Dirac's proposition. We provide a natural formulation of classical mechanics through noncommutative quantities with a non-zero Planck constant. This is done with the help of the nilpotent unit, which squares to zero. Thus, the crucial r\\^ole in quantum theory shall be attributed to the usage of complex numbers. The paper provides English and Russian versions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-18T11:20:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81P05",
      "22E27"
    ],
    "keywords": [
      "quantum mechanics",
      "classical mechanics",
      "critically review diracs proposition",
      "non-zero planck constant",
      "natural formulation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.1858K"
    }
  }
}