{
  "annotation_id": "875e5225-3a2a-4df2-8bf2-43b3b0de306b",
  "date_created": "2026-03-02T18:01:59.930000Z",
  "date_modified": "2026-03-02T18:01:59.930000Z",
  "file_hash": "6147a7842ae3a34c95dcffbffe6c51b52743b77db8876ee774805e1015440e56",
  "private": false,
  "record": {
    "abstract": "For the creation operator $\\adag $ and the annihilation operator $a$ of a\nharmonic oscillator, we consider Weyl ordering expression of $(\\adag a)^n$ and\nobtain a new symmetric expression of Weyl ordering w.r.t. $\\adag a \\equiv N$\nand $a\\adag =N+1$ where $N$ is the number operator. Moreover, we interpret\nintertwining formulas of various orderings in view of the difference theory.\nThen we find that the noncommutative parameter corresponds to the increment of\nthe difference operator w.r.t. variable $N$. Therefore, quantum\n(noncommutative) calculations of harmonic oscillators are done by classical\n(commutative) ones of the number operator by using the difference theory. As a\nby-product, nontrivial relations including the Stirling number of the first\nkind are also obtained.",
    "arxiv_id": "quant-ph/0304094",
    "authors": [
      "Kazuyuki Fujii",
      "Tatsuo Suzuki"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1142/S021773230401374X",
    "journal_ref": "Mod.Phys.Lett. A19 (2004) 827-840",
    "title": "A New Symmetric Expression of Weyl Ordering",
    "url": "https://arxiv.org/abs/quant-ph/0304094"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "db600960-ce14-46dc-95d4-e700a958a8ca",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}