{
  "id": "1111.7043",
  "version": "v2",
  "published": "2011-11-30T03:31:11.000Z",
  "updated": "2012-06-16T11:26:18.000Z",
  "title": "The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time",
  "authors": [
    "Matthew F. Brown"
  ],
  "comment": "21 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "physics.hist-ph",
    "quant-ph"
  ],
  "abstract": "Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic process arises from the quantization of the clock, and this is derived naturally from the matrix-algebra representation of the nilpotent Newton-Leibniz time differential [Belavkin]. It is observed that this condition expectation is a rigorous formulation of the Feynman Path Integral.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-16T11:26:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81P05"
    ],
    "keywords": [
      "hamiltonian dynamics",
      "stochastic representation",
      "quantization",
      "nilpotent newton-leibniz time differential",
      "stochastic process arises"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.7043B"
    }
  }
}