{
  "annotation_id": "1db4476b-f191-4f58-8cc9-0402e3690b2f",
  "date_created": "2026-03-02T18:01:38.407000Z",
  "date_modified": "2026-03-02T18:01:38.407000Z",
  "file_hash": "dc7f08723822b20ea4a1ef822621d48ec1b07a35644474641563ef2aad61f1a8",
  "private": false,
  "record": {
    "abstract": "A gauge invariant quantization in a closed integral form is developed over a\nlinear phase space endowed with an inhomogeneous Faraday electromagnetic\ntensor. An analog of the Groenewold product formula (corresponding to Weyl\nordering) is obtained via a membrane magnetic area, and extended to the product\nof N symbols. The problem of ordering in quantization is related to different\nconfigurations of membranes: a choice of configuration determines a phase\nfactor that fixes the ordering and controls a symplectic groupoid structure on\nthe secondary phase space. A gauge invariant solution of the quantum evolution\nproblem for a charged particle in an electromagnetic field is represented in an\nexact continual form and in the semiclassical approximation via the area of\ndynamical membranes.",
    "arxiv_id": "quant-ph/0002041",
    "authors": [
      "M. V. Karasev",
      "T. A. Osborn"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1426688",
    "journal_ref": "J. Math. Phys. 43:756-788, 2002",
    "title": "Symplectic areas, quantization, and dynamics in electromagnetic fields",
    "url": "https://arxiv.org/abs/quant-ph/0002041"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "efc43954-6ad1-4b6a-aa70-5c4ef5b7f74b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}