{
  "id": "quant-ph/0305012",
  "version": "v2",
  "published": "2003-05-02T11:15:24.000Z",
  "updated": "2003-10-17T12:10:43.000Z",
  "title": "Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation",
  "authors": [
    "N. Mukunda",
    "Arvind",
    "S. Chaturvedi",
    "R. Simon"
  ],
  "comment": "Latex, 54 pages, Section VII enlarged, new references added",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar Cartesian case are systematically generalised to accommodate new features which arise when the configuration space changes from $n$-dimensional Euclidean space ${\\cal R}^n$ to a Lie group $G$. The notion of canonical momentum is carefully analysed, and the meanings of marginal probability distributions and their recovery from the Wigner distribution are clarified. For the case of compact $G$ an explicit definition of the Wigner distribution is proposed, possessing all the required properties. Geodesic curves in $G$ which help introduce a notion of the `mid point' of two group elements play a central role in the construction.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-10-17T12:10:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Fd",
      "02.20.Qs",
      "02.50.Ng",
      "02.50.Cw",
      "02.40.Hw"
    ],
    "keywords": [
      "wigner distribution",
      "lie group",
      "regular representation",
      "quantum mechanics",
      "familiar cartesian case"
    ],
    "publication": {
      "doi": "10.1063/1.1631393",
      "journal": "Journal of Mathematical Physics",
      "year": 2004,
      "month": "Jan",
      "volume": 45,
      "number": 1,
      "pages": 114
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004JMP....45..114M"
    }
  }
}