{
  "annotation_id": "45168e47-1541-4a09-a19e-6a96c4671c4d",
  "date_created": "2026-03-02T18:02:23.431000Z",
  "date_modified": "2026-03-02T18:02:23.431000Z",
  "file_hash": "1b65b2b0017f1da7f47cd185be0c47b73f94b8897d1b397e9b85f5d8d068420b",
  "private": false,
  "record": {
    "abstract": "The well known Poisson Summation Formula is analysed from the perspective of\nthe coherent state systems associated with the Heisenberg--Weyl group. In\nparticular, it is shown that the Poisson summation formula may be viewed\nabstractly as a relation between two sets of bases (Zak bases) arising as\nsimultaneous eigenvectors of two commuting unitary operators in which geometric\nphase plays a key role. The Zak bases are shown to be interpretable as\ngeneralised coherent state systems of the Heisenberg--Weyl group and this, in\nturn, prompts analysis of the sampling theorem (an important and useful\nconsequence of the Poisson Summation Formula) and its extension from a coherent\nstate point of view leading to interesting results on properties of von Neumann\nand finer lattices based on standard and generalised coherent state systems.",
    "arxiv_id": "quant-ph/0601059",
    "authors": [
      "Arvind",
      "S. Chaturvedi",
      "N. Mukunda",
      "R. Simon"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0031-8949/74/2/004",
    "title": "The Sampling Theorem and Coherent State Systems in Quantum Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0601059"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6e186648-3184-4ebb-ad0a-49f72679e0d4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}