{
  "annotation_id": "d8b8af5f-ccc2-4c96-90d2-6c8016c74f63",
  "date_created": "2026-03-02T18:01:28.008000Z",
  "date_modified": "2026-03-02T18:01:28.008000Z",
  "file_hash": "c16d3ef374514d7e73706bf11f07000d2f092b5f13cfdb3a25b4d4c8f5f069dd",
  "private": false,
  "record": {
    "abstract": "Generalizing the case of the usual harmonic oscillator, we look for Bargmann\nrepresentations corresponding to deformed harmonic oscillators. Deformed\nharmonic oscillator algebras are generated by four operators $a, a^\\dagger, N$\nand the unity 1 such as $[a,N] = a, [a^\\dagger,N] = -a^\\dagger$, $a^\\dagger a =\n\\psi(N)$ and $aa^\\dagger =\\psi(N+1)$. We discuss the conditions of existence of\na scalar product expressed with a true integral on the space spanned by the\neigenstates of $a$ (or $a^\\dagger$). We give various examples, in particular we\nconsider functions $\\psi$ that are linear combinations of $q^N$, $q^{-N}$ and\nunity and that correspond to q-oscillators with Fock-representations or with\nnon-Fock-representations.",
    "arxiv_id": "q-alg/9707020",
    "authors": [
      "M. Irac-Astaud",
      "G. Rideau"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1142/S0129055X98000343",
    "title": "Bargmann representations for deformed harmonic oscillators",
    "url": "https://arxiv.org/abs/q-alg/9707020"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8131a188-7815-49c4-8d8b-51373b599020",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}