{
  "id": "1002.2061",
  "version": "v4",
  "published": "2010-02-10T10:38:14.000Z",
  "updated": "2010-12-18T09:04:07.000Z",
  "title": "A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. II : Supmech and Quantum Systems",
  "authors": [
    "Tulsi Dass"
  ],
  "comment": "55 pages; some modifications in text; improved treatment of topological aspects and of Noether invariants; results unchanged",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Supmech, which is noncommutative Hamiltonian mechanics \\linebreak (NHM) (developed in paper I) with two extra ingredients : positive observable valued measures (PObVMs) [which serve to connect state-induced expectation values and classical probabilities] and the `CC condition' [which stipulates that the sets of observables and pure states be mutually separating] is proposed as a universal mechanics potentially covering all physical phenomena. It facilitates development of an autonomous formalism for quantum mechanics. Quantum systems, defined algebraically as supmech Hamiltonian systems with non-supercommutative system algebras, are shown to inevitably have Hilbert space based realizations (so as to accommodate rigged Hilbert space based Dirac bra-ket formalism), generally admitting commutative superselection rules. Traditional features of quantum mechanics of finite particle systems appear naturally. A treatment of localizability much simpler and more general than the traditional one is given. Treating massive particles as localizable elementary quantum systems, the Schr$\\ddot{o}$dinger wave functions with traditional Born interpretation appear as natural objects for the description of their pure states and the Schr$\\ddot{o}$dinger equation for them is obtained without ever using a classical Hamiltonian or Lagrangian. A provisional set of axioms for the supmech program is given.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-12-18T09:04:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51P05",
      "81P99"
    ],
    "keywords": [
      "quantum systems",
      "hilberts sixth problem",
      "stepwise planned approach",
      "pure states",
      "quantum mechanics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1142/S0219581X10006594",
      "journal": "International Journal of Nanoscience",
      "year": 2010,
      "number": 3,
      "pages": 201
    },
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 922109,
      "adsabs": "2010IJN.....9..201D"
    }
  }
}