{
  "annotation_id": "6017d0fe-ad78-4eb0-8f97-502caf69620b",
  "date_created": "2026-03-02T18:01:28.652000Z",
  "date_modified": "2026-03-02T18:01:28.652000Z",
  "file_hash": "23f4538218df31879f9cec7f7e7595dd4836d943c372ca71aa9f8e9924490bed",
  "private": false,
  "record": {
    "abstract": "A recursive deformation of the boson commutation relation is introduced. Each\nstep consists of a minimal deformation of a commutator\n$[a,\\ad]=f_k(\\cdots;\\no)$ into $[a,\\ad]_{q_{k+1}}=f_k(\\cdots;\\no)$, where\n$\\cdots$ stands for the set of deformation parameters that $f_k$ depends on,\nfollowed by a transformation into the commutator $[a,\\ad]=f_{k+1}(\\cdots,\\,\nq_{k+1};\\no)$ to which the deformed commutator is equivalent within the Fock\nspace. Starting from the harmonic oscillator commutation relation $[a,\\ad]=1$\nwe obtain the Arik-Coon and the Macfarlane-Biedenharn oscillators at the first\nand second steps, respectively, followed by a sequence of multiparameter\ngeneralizations. Several other types of deformed commutation relations related\nto the treatment of integrable models and to parastatistics are also obtained.\nThe ``generic\u0027\u0027 form consists of a linear combination of exponentials of the\nnumber operator, and the various recursive families can be classified according\nto the number of free linear parameters involved, that depends on the form of\nthe initial commutator.",
    "arxiv_id": "q-alg/9512032",
    "authors": [
      "J. Katriel",
      "C. Quesne"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "doi": "10.1063/1.531475",
    "journal_ref": "J.Math.Phys. 37 (1996) 1650-1661",
    "title": "Recursively minimally-deformed oscillators",
    "url": "https://arxiv.org/abs/q-alg/9512032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c472eb35-18b8-495d-9799-fad25acc6f8d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}