{
  "annotation_id": "8a861a64-6f7f-4e1c-9124-658da74b9a1a",
  "date_created": "2026-03-02T18:02:06.456000Z",
  "date_modified": "2026-03-02T18:02:06.456000Z",
  "file_hash": "b5bd90c164b06c4240792477a63546b435e897221d1533bd241b7b428cb75dc4",
  "private": false,
  "record": {
    "abstract": "Mathematical method of quantum phase space is very useful in physical\napplications like quantum optics and non-relativistic quantum mechanics.\nHowever, attempts to generalize it for the relativistic case lead to some\ndifficulties. One of problems is band structure of energy spectrum for a\nrelativistic particle. This corresponds to an internal degree of freedom,\nso-called charge variable. In physical problems we often deal with such of\ndynamical variables that do not depend on this degree of freedom. These are\nposition, momentum, and any combination of them. Restricting our consideration\nto this kind of observables we propose the relativistic Weyl--Wigner--Moyal\nformalism that contains some surprising differences from its non-relativistic\ncounterpart.",
    "arxiv_id": "quant-ph/0402140",
    "authors": [
      "A. A. Semenov",
      "B. I. Lev",
      "C. V. Usenko"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "journal_ref": "EconfC0306234:1448-1453,2003",
    "title": "Quantum Phase Space in Relativistic Theory: the Case of Charge-Invariant   Observables",
    "url": "https://arxiv.org/abs/quant-ph/0402140"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5b44ec36-8207-4937-81e8-118a65fee939",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}