{
  "annotation_id": "45bf07b4-3139-4541-bb2b-448b4e18ee3f",
  "date_created": "2026-03-02T18:01:49.224000Z",
  "date_modified": "2026-03-02T18:01:49.224000Z",
  "file_hash": "21f38778bbec3fa9259858f04646241fccb9f6512cb2cb20438f79b0efea0b18",
  "private": false,
  "record": {
    "abstract": "We provide geometric quantization of a completely integrable Hamiltonian\nsystem in the action-angle variables around an invariant torus with respect to\npolarization spanned by almost-Hamiltonian vector fields of angle variables.\nThe associated quantum algebra consists of functions affine in action\ncoordinates. We obtain a set of its nonequivalent representations in the\nseparable pre-Hilbert space of smooth complex functions on the torus where\naction operators and a Hamiltonian are diagonal and have countable spectra.",
    "arxiv_id": "quant-ph/0112083",
    "authors": [
      "G. Giachetta",
      "L. Mangiarotti",
      "G. Sardanashvily"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/S0375-9601(02)00956-8",
    "title": "Geometric quantization of completely integrable Hamiltonian systems in   the action-angle variables",
    "url": "https://arxiv.org/abs/quant-ph/0112083"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "889aa199-4767-4c6b-8329-5ee6c65192a6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}