{
  "annotation_id": "03c821dc-22a6-40f9-ac3d-18e74bca16a8",
  "date_created": "2026-03-02T18:02:41.172000Z",
  "date_modified": "2026-03-02T18:02:41.172000Z",
  "file_hash": "05f6de0c58f8616df08890bfcfd61b7639443b02298f6b349e64722559d537f2",
  "private": false,
  "record": {
    "abstract": "This paper presents some methods of representing canonical commutation\nrelations in terms of hyperfinite-dimensional matrices, which are constructed\nby nonstandard analysis. The first method uses representations of a nonstandard\nextension of finite Heisenberg group, called hyperfinite Heisenberg group. The\nsecond is based on hyperfinite-dimensional representations of so(3). Then, the\ncases of infinite degree of freedom are argued in terms of the algebra of\nhyperfinite parafermi oscillators, which is mathematically equivalent to a\nhyperfinite-dimensional representation of so(n).",
    "arxiv_id": "quant-ph/9706008",
    "authors": [
      "Hideyasu Yamashita"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.532413",
    "journal_ref": "J.Math.Phys. 39 (1998) 2682-2692",
    "title": "Hyperfinite-Dimensional Representations of Canonical Commutation   Relation",
    "url": "https://arxiv.org/abs/quant-ph/9706008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0bd0de36-2bd3-46c4-80cc-87f195d478f3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}