{
  "annotation_id": "db171b31-8889-4d0d-83d7-e8ee2d85f515",
  "date_created": "2026-03-02T18:02:37.509000Z",
  "date_modified": "2026-03-02T18:02:37.509000Z",
  "file_hash": "abefa88a77a6cf1764fdc0df98d1a2aed3c21949cbf0afa20e26b1669f289771",
  "private": false,
  "record": {
    "abstract": "We show that an unambiguous and correct quantization of the second-class\nconstrained system of a free particle on a sphere in $D$ dimensions is possible\nonly by converting the constraints to abelian gauge constraints, which are of\nfirst class in Dirac\u0027s classification scheme. The energy spectrum is equal to\nthat of a pure Laplace-Beltrami operator with no additional constant arising\nfrom the curvature of the sphere. A quantization of Dirac\u0027s modified Poisson\nbrackets for second-class constraints is also possible and unique, but must be\nrejected since the resulting energy spectrum is physically incorrect.",
    "arxiv_id": "quant-ph/9702006",
    "authors": [
      "Hagen Kleinert",
      "Sergei V. Shabanov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/S0375-9601(97)00410-6",
    "journal_ref": "Phys.Lett. A232 (1997) 327-332",
    "title": "Proper Dirac Quantization of Free Particle on D-Dimensional Sphere",
    "url": "https://arxiv.org/abs/quant-ph/9702006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "554523e2-46df-40c8-8030-525186f39e48",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}