{
  "annotation_id": "ab46d735-a2a0-4de4-9acd-878f98f34a77",
  "date_created": "2026-03-02T18:02:00.260000Z",
  "date_modified": "2026-03-02T18:02:00.260000Z",
  "file_hash": "42e6143d42d3dddd67f1b6689bf7d60b5e82546c6dc0638fbba8e691f578ddc1",
  "private": false,
  "record": {
    "abstract": "The orbit method of Kirillov is used to derive the p-mechanical brackets\n[quant-ph/0212101]. They generate the quantum (Moyal) and classic (Poisson)\nbrackets on respective orbits corresponding to representations of the\nHeisenberg group. The extension of p-mechanics to field theory is made through\nthe De Donder-Weyl Hamiltonian formulation. The principal step is the\nsubstitution of the Heisenberg group with Galilean. Keywords: Classic and\nquantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg\ngroup, orbit method, deformation quantisation, representation theory, De\nDonder-Weyl field theory, Galilean group, Clifford algebra, conformal M\\\"obius\ntransformation, Dirac operator",
    "arxiv_id": "quant-ph/0306101",
    "authors": [
      "Vladimir V. Kisil"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Proc. Inst. of Maths of NAS of Ukraine, 50:1108-1115 (2004)",
    "title": "p-Mechanics and De Donder-Weyl Theory",
    "url": "https://arxiv.org/abs/quant-ph/0306101"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e94099d2-0536-40be-b6a5-e750b81fbf21",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}