{
  "id": "quant-ph/0312051",
  "version": "v1",
  "published": "2003-12-05T13:29:12.000Z",
  "updated": "2003-12-05T13:29:12.000Z",
  "title": "The general structure and ergodic properties of quantum and classical mechanics: A unified C*-algebraic approach",
  "authors": [
    "Rocco Duvenhage"
  ],
  "comment": "PhD thesis, University of Pretoria, May 2002, 87 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical formulation of both can be expressed in terms of unital C*-algebras, in which case it becomes clear that they have the same general structure, with quantum mechanics a noncommutative generalization of the classical case. In purely mathematical terms it is seen that quantum mechanics is a noncommutative generalization of probability theory. The most important insight in this respect is that the projection postulate of quantum mechanics is a noncommutative conditional probability. This is the subject of Chapter 1 of the thesis. As ergodic theory (the long term behaviour of a dynamical system) is done in classical probability theory, it is then also done for noncommutative probability theory in Chapter 2. In particular, generalizations of Khintchine's recurrence theorem and a variation thereof for ergodic systems are proved, as well as various characterizations of noncommutative ergodicity. Lastly, in Chapter 3, recurrence and ergodicity is then investigated from a physical perspective in quantum and classical mechanics, by means of a quantum mechanical analogue of Liouville's Theorem in classical mechanics which was suggested in Chapter 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-05T13:29:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical mechanics",
      "general structure",
      "ergodic properties",
      "quantum mechanics",
      "probability theory"
    ],
    "tags": [
      "dissertation"
    ],
    "publication": {
      "journal": "Ph.D. Thesis",
      "year": 2003,
      "month": "Dec"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 87,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003PhDT.......141D"
    }
  }
}