{
  "annotation_id": "72bf9fde-8b0c-4c42-997d-d76b8261f926",
  "date_created": "2026-03-02T18:02:06.438000Z",
  "date_modified": "2026-03-02T18:02:06.438000Z",
  "file_hash": "ad416a0c247a55e451bf455965dd35a8f9ea9b832851b8357141e72aa330cb58",
  "private": false,
  "record": {
    "abstract": "The orbit method of Kirillov is used to derive the p-mechanical brackets\n[math-ph/0007030, quant-ph/0212101]. They generate the quantum (Moyal) and\nclassic (Poisson) brackets on respective orbits corresponding to\nrepresentations of the Heisenberg group. The extension of p-mechanics to field\ntheory is made through the De Donder--Weyl Hamiltonian formulation. The\nprincipal step is the substitution of the Heisenberg group with Galilean.\n  Keywords: Classic and quantum mechanics, Moyal brackets, Poisson brackets,\ncommutator, Heisenberg group, orbit method, deformation quantisation,\nrepresentation theory, De Donder--Weyl field theory, Galilean group, Clifford\nalgebra, conformal M\\\"obius transformation, Dirac operator.",
    "arxiv_id": "quant-ph/0402035",
    "authors": [
      "Vladimir V. Kisil"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/S0034-4877(05)80068-0",
    "journal_ref": "Rept.Math.Phys. 56 (2005) 161-174",
    "title": "p-Mechanics and Field Theory",
    "url": "https://arxiv.org/abs/quant-ph/0402035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dc81a132-5b1a-4882-acf7-e9d829a6fa57",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}