{
  "annotation_id": "220728da-afa4-4daf-bee3-2de41fb09b15",
  "date_created": "2026-03-02T18:02:37.787000Z",
  "date_modified": "2026-03-02T18:02:37.787000Z",
  "file_hash": "60e8b46f33a4f4e2570618d6c7fcf0eafdac7c4c35ba750bf69bdda18a5672f1",
  "private": false,
  "record": {
    "abstract": "We consider two analytic representations of the SU(1,1) Lie group: the\nrepresentation in the unit disk based on the SU(1,1) Perelomov coherent states\nand the Barut-Girardello representation based on the eigenstates of the SU(1,1)\nlowering generator. We show that these representations are related through a\nLaplace transform. A ``weak\u0027\u0027 resolution of the identity in terms of the\nPerelomov SU(1,1) coherent states is presented which is valid even when the\nBargmann index $k$ is smaller than one half. Various applications of these\nresults in the context of the two-photon realization of SU(1,1) in quantum\noptics are also discussed.",
    "arxiv_id": "quant-ph/9607022",
    "authors": [
      "C. Brif",
      "A. Vourdas",
      "A. Mann"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/29/18/017",
    "journal_ref": "J.Phys.A29:5873-5886,1996",
    "title": "Analytic representations based on SU(1,1) coherent states and their   applications",
    "url": "https://arxiv.org/abs/quant-ph/9607022"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "210da538-b6a4-4324-a57f-bd4093e7c994",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}