{
  "annotation_id": "763333fa-481a-497a-9289-c7e43de51351",
  "date_created": "2026-03-02T18:02:37.577000Z",
  "date_modified": "2026-03-02T18:02:37.577000Z",
  "file_hash": "34f540c6ad7a28a0506b268788a2d3a3ff97d0c7de9c6aa1a304142f8febaebf",
  "private": false,
  "record": {
    "abstract": "`Umbral calculus\u0027 deals with representations of the canonical commutation\nrelations. We present a short exposition of it and discuss how this calculus\ncan be used to discretize continuum models and to construct representations of\nLie algebras on a lattice. Related ideas appeared in recent publications and we\nshow that the examples treated there are special cases of umbral calculus. This\nobservation then suggests various generalizations of these examples. A special\numbral representation of the canonical commutation relations given in terms of\nthe position and momentum operator on a lattice is investigated in detail.",
    "arxiv_id": "quant-ph/9509014",
    "authors": [
      "A. Dimakis",
      "F. Mueller-Hoissen",
      "T. Striker"
    ],
    "categories": [
      "quant-ph",
      "hep-lat",
      "hep-th"
    ],
    "doi": "10.1088/0305-4470/29/21/017",
    "journal_ref": "J.Phys.A29:6861-6876,1996",
    "title": "Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice",
    "url": "https://arxiv.org/abs/quant-ph/9509014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "405b2b81-6ec5-4d39-8357-c07a5c27a9b5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}