{
  "annotation_id": "b6586592-0bd7-49f2-9dab-e6ae32f86c03",
  "date_created": "2026-03-02T18:02:20.700000Z",
  "date_modified": "2026-03-02T18:02:20.700000Z",
  "file_hash": "1bc956e723af82dc04a92444bbd551adacbd2606555676cae0b2c2c190f841b7",
  "private": false,
  "record": {
    "abstract": "We solve the boson normal ordering problem for $(q(a^\\dag)a+v(a^\\dag))^n$\nwith arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and\n$a^\\dag$ are boson annihilation and creation operators, satisfying\n$[a,a^\\dag]=1$. This consequently provides the solution for the exponential\n$e^{\\lambda(q(a^\\dag)a+v(a^\\dag))}$ generalizing the shift operator. In the\ncourse of these considerations we define and explore the monomiality principle\nand find its representations. We exploit the properties of Sheffer-type\npolynomials which constitute the inherent structure of this problem. In the end\nwe give some examples illustrating the utility of the method and point out the\nrelation to combinatorial structures.",
    "arxiv_id": "quant-ph/0510079",
    "authors": [
      "K A Penson",
      "P Blasiak",
      "G Dattoli",
      "G H E Duchamp",
      "A Horzela",
      "A I Solomon"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/1742-6596/30/1/012",
    "journal_ref": "J. Phys.: Conf. Ser. 30: 86-97, 2006",
    "title": "Monomiality principle, Sheffer-type polynomials and the normal ordering   problem",
    "url": "https://arxiv.org/abs/quant-ph/0510079"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d82005cf-477f-48e9-9b5f-433957dab253",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}