{
  "annotation_id": "480a8035-3e66-41ba-a763-2b8e3f90dd85",
  "date_created": "2026-03-02T18:02:00.201000Z",
  "date_modified": "2026-03-02T18:02:00.201000Z",
  "file_hash": "5230a1b2ff20dd5436db3e159fc6550be75243bf03373644935c50384d366bb1",
  "private": false,
  "record": {
    "abstract": "Nambu\u0027s construction of multi-linear brackets for super-integrable systems\ncan be thought of as degenerate Poisson brackets with a maximal set of Casimirs\nin their kernel. By introducing privileged coordinates in phase space these\ndegenerate Poisson brackets are brought to the form of Heisenberg\u0027s equations.\nWe propose a definition for constructing quantum operators for classical\nfunctions which enables us to turn the maximally degenerate Poisson brackets\ninto operators. They pose a set of eigenvalue problems for a new state vector.\nThe requirement of the single valuedness of this eigenfunction leads to\nquantization. The example of the harmonic oscillator is used to illustrate this\ngeneral procedure for quantizing a class of maximally super-integrable systems.",
    "arxiv_id": "quant-ph/0306059",
    "authors": [
      "Y. Nutku"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "nlin.SI"
    ],
    "doi": "10.1088/0305-4470/36/27/308",
    "journal_ref": "J.Phys.A36:7559-7568,2003",
    "title": "Quantization with maximally degenerate Poisson brackets: The harmonic   oscillator!",
    "url": "https://arxiv.org/abs/quant-ph/0306059"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "10c34174-2146-44ff-ad24-d333f5202c69",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}