{
  "annotation_id": "b2d92727-b6c3-4c31-8160-a7e19f799b3d",
  "date_created": "2026-03-02T18:02:10.107000Z",
  "date_modified": "2026-03-02T18:02:10.107000Z",
  "file_hash": "360bd671c7f6c9da0253900532a4f0c66089a9e6a95e84a709c4b441d75d9061",
  "private": false,
  "record": {
    "abstract": "In quantum mechanics the kinetic energy term for a single particle is usually\nwritten in the form of the Laplace-Beltrami operator. This operator is a factor\nordering of the classical kinetic energy. We investigate other relatively\nsimple factor orderings and show that the {\\it only} other solution for a\nconformally flat metric is the conformally invariant Laplace-Beltrami operator.\nFor non-conformally-flat metrics this type of factor ordering fails, by just\none term, to give the conformally invariant Laplace-Beltrami operator.",
    "arxiv_id": "quant-ph/0406167",
    "authors": [
      "Michael P. Ryan, Jr.",
      "Alexander V. Turbiner"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/j.physleta.2004.10.021",
    "journal_ref": "Phys.Lett. A333 (2004) 30-34",
    "title": "The conformally invariant Laplace-Beltrami operator and factor ordering",
    "url": "https://arxiv.org/abs/quant-ph/0406167"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0865e47b-e002-4be9-9cc4-4279b3ebc944",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}