{
  "id": "quant-ph/9902064",
  "version": "v1",
  "published": "1999-02-18T15:47:54.000Z",
  "updated": "1999-02-18T15:47:54.000Z",
  "title": "Formulation of the Classical Mechanics in the Ring of Operators",
  "authors": [
    "A. Vercin"
  ],
  "comment": "14 Pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "By making use of the Weyl-Wigner-Groenewold-Moyal association rules, a commutative product and a new quantum bracket are constructed in the ring of operators \\cal{F}(H). In this way, an isomorphism between Lie algebra of classical observables (with Poisson bracket) and the Lie algebra of quantum observables with this new bracket is established. By these observations, a formulation of the classical mechanics in \\cal{F}(H} is obtained and is shown to be \\hbar\\to 0 limit of the Heisenberg picture formulation of the quantum mechanics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-02-18T15:47:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical mechanics",
      "lie algebra",
      "heisenberg picture formulation",
      "weyl-wigner-groenewold-moyal association rules",
      "quantum observables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 495550,
      "adsabs": "1999quant.ph..2064V"
    }
  }
}