{
  "annotation_id": "1490463f-31cd-40c4-bb8c-93691bf5146a",
  "date_created": "2026-03-02T18:02:16.218000Z",
  "date_modified": "2026-03-02T18:02:16.218000Z",
  "file_hash": "4aeb2cf3c175162b9285667c8d718a59c4f338ce95b03b41de011e20d6b1934c",
  "private": false,
  "record": {
    "abstract": "This is a challenging paper including some review and new results.\n  Since the non-commutative version of the classical system based on the\ncompact group SU(2) has been constructed in (quant-ph/0502174) by making use of\nJaynes-Commings model and so-called Quantum Diagonalization Method in\n(quant-ph/0502147), we construct a non-commutative version of the classical\nsystem based on the non-compact group SU(1,1) by modifying the compact case.\n  In this model the Hamiltonian is not hermite but pseudo hermite, which causes\na big difference between two models. For example, in the classical\nrepresentation theory of SU(1,1), unitary representations are infinite\ndimensional from the starting point. Therefore, to develop a unitary theory of\nnon-commutative system of SU(1,1) we need an infinite number of non-commutative\nsystems, which means a kind of {\\bf second non-commutativization}. This is a\nvery hard and interesting problem.\n  We develop a corresponding theory though it is not always enough, and present\nsome challenging problems concerning how classical properties can be extended\nto the non-commutative case.\n  This paper is arranged for the convenience of readers as the first subsection\nis based on the standard model (SU(2) system) and the next one is based on the\nnon-standard model (SU(1,1) system). This contrast may make the similarity and\ndifference between the standard and non-standard models clear.",
    "arxiv_id": "quant-ph/0506026",
    "authors": [
      "Kazuyuki Fujii"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1142/S0219887805000879",
    "journal_ref": "Int.J.Geom.Meth.Mod.Phys.2:783,2005",
    "title": "Standard and Non-Standard Quantum Models : A Non-Commutative Version of   the Classical System of SU(2) and SU(1,1) Arising from Quantum Optics",
    "url": "https://arxiv.org/abs/quant-ph/0506026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "340d2518-1d2a-463a-b94f-877403174008",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}