{
  "annotation_id": "db604530-e965-47ca-b012-8e5884b185f3",
  "date_created": "2026-03-02T18:02:40.650000Z",
  "date_modified": "2026-03-02T18:02:40.650000Z",
  "file_hash": "c0de621352a3b9c68be108a126ae1f2e99114e6faad59cc2b0b9c6f6cae61f99",
  "private": false,
  "record": {
    "abstract": "Elements of the quantization in field theory based on the covariant\npolymomentum Hamiltonian formalism (the De Donder-Weyl theory), a possibility\nof which was originally discussed in 1934 by Born and Weyl, are developed. The\napproach is based on a recently proposed graded Poisson bracket on differential\nforms in field theory (see e.g. hep-th/9709229). A covariant analogue of the\nSchr\\\"odinger equation for a hypercomplex wave function on the space of field\nand space-time variables is put forward. It is shown to lead to the De\nDonder-Weyl Hamilton-Jacobi equations in quasiclassical limit. A possible\nrelation to the functional Schr\\\"odinger picture in quantum field theory is\noutlined.",
    "arxiv_id": "quant-ph/9712058",
    "authors": [
      "Igor V. Kanatchikov"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "journal_ref": "Int.J.Theor.Phys. 37 (1998) 333-342",
    "title": "Towards the Born-Weyl Quantization of Fields",
    "url": "https://arxiv.org/abs/quant-ph/9712058"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6aa078a0-3285-4f5e-a86d-b7ff1bbcd933",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}