{
  "annotation_id": "98ca7bb1-2247-4bf6-944c-1a5c468d844c",
  "date_created": "2026-03-02T18:02:00.272000Z",
  "date_modified": "2026-03-02T18:02:00.272000Z",
  "file_hash": "209c338b6f47160ef68300920b4632b61569ce88b9cf41a4afafc9cfd54cffb4",
  "private": false,
  "record": {
    "abstract": "We consider the problem of setting up the Wigner distribution for states of a\nquantum system whose configuration space is a Lie group. The basic properties\nof Wigner distributions in the familiar Cartesian case are systematically\ngeneralised to accommodate new features which arise when the configuration\nspace changes from $n$-dimensional Euclidean space ${\\cal R}^n$ to a Lie group\n$G$. The notion of canonical momentum is carefully analysed, and the meanings\nof marginal probability distributions and their recovery from the Wigner\ndistribution are clarified. For the case of compact $G$ an explicit definition\nof the Wigner distribution is proposed, possessing all the required properties.\nGeodesic curves in $G$ which help introduce a notion of the `mid point\u0027 of two\ngroup elements play a central role in the construction.",
    "arxiv_id": "quant-ph/0305012",
    "authors": [
      "N. Mukunda",
      "Arvind",
      "S. Chaturvedi",
      "R. Simon"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1631393",
    "title": "Wigner distributions and quantum mechanics on Lie groups: the case of   the regular representation",
    "url": "https://arxiv.org/abs/quant-ph/0305012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7a753e24-2d48-4ada-8306-d96b668b800c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}