{
  "annotation_id": "f8fcb055-ff9f-47b5-a99b-635d8dcf0410",
  "date_created": "2026-03-02T18:02:20.693000Z",
  "date_modified": "2026-03-02T18:02:20.693000Z",
  "file_hash": "0788415c9ba5f1b7a5dd36d546c9660812de3a56bbe6b600bdebf6898d200ff3",
  "private": false,
  "record": {
    "abstract": "A Hilbert space in M dimensions is shown explicitly to accommodate\nrepresentations that reflect the prime numbers decomposition of M.\nRepresentations that exhibit the factorization of M into two relatively prime\nnumbers: the kq representation (J. Zak, Phys. Today, {\\bf 23} (2), 51 (1970)),\nand related representations termed $q_{1}q_{2}$ representations (together with\ntheir conjugates) are analysed, as well as a representation that exhibits the\ncomplete factorization of M. In this latter representation each quantum number\nvaries in a subspace that is associated with one of the prime numbers that make\nup M.",
    "arxiv_id": "quant-ph/0508191",
    "authors": [
      "M. Revzen",
      "F. C. Khanna",
      "A. Mann",
      "J. Zak"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/39/18/027",
    "title": "Factorizations and Physical Representations",
    "url": "https://arxiv.org/abs/quant-ph/0508191"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a0d08983-e0ca-4393-b780-5ba12cae124d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}