{
  "annotation_id": "805d779d-b8a2-4d80-9f2b-07753227ca19",
  "date_created": "2026-03-02T18:02:38.118000Z",
  "date_modified": "2026-03-02T18:02:38.118000Z",
  "file_hash": "5e27441d0fb8de6760ee4a7864f6265932e49fc338c5fcf4d1fa360a7cd31b55",
  "private": false,
  "record": {
    "abstract": "Following the relationship between probability distribution and coherent\nstates, for example the well known Poisson distribution and the ordinary\ncoherent states and relatively less known one of the binomial distribution and\nthe $su(2)$ coherent states, we propose ``interpretation\u0027\u0027 of $su(1,1)$ and\n$su(r,1)$ coherent states ``in terms of probability theory\u0027\u0027. They will be\ncalled the ``negative binomial\u0027\u0027 (``multinomial\u0027\u0027) ``states\u0027\u0027 which correspond\nto the ``negative\u0027\u0027 binomial (multinomial) distribution, the non-compact\ncounterpart of the well known binomial (multinomial) distribution. Explicit\nforms of the negative binomial (multinomial) states are given in terms of\nvarious boson representations which are naturally related to the probability\ntheory interpretation. Here we show fruitful interplay of probability theory,\ngroup theory and quantum theory.",
    "arxiv_id": "quant-ph/9610022",
    "authors": [
      "Hong-Chen Fu",
      "Ryu Sasaki"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.532102",
    "journal_ref": "J.Math.Phys. 38 (1997) 3968-3987",
    "title": "Negative Binomial and Multinomial States: probability distributions and   coherent states",
    "url": "https://arxiv.org/abs/quant-ph/9610022"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fedd29fa-971d-4c6e-ac5b-475ac1e29f58",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}