{
  "annotation_id": "1d0d679f-d56b-4a1d-b147-be508459022b",
  "date_created": "2026-03-02T18:01:56.190000Z",
  "date_modified": "2026-03-02T18:01:56.190000Z",
  "file_hash": "b9f891a132eef696e77aed9eafbdb22936343eba504e0c6d9f0a852d90ab662b",
  "private": false,
  "record": {
    "abstract": "We derive explicit semiclassical quantisation conditions for the Dirac and\nPauli equations. We show that the spin degree of freedom yields a contribution\nwhich is of the same order of magnitude as the Maslov correction in\nEinstein-Brillouin-Keller quantisation. In order to obtain this result a\ngeneralisation of the notion of integrability for a certain skew product flow\nof classical translational dynamics and classical spin precession has to be\nderived. Among the examples discussed is the relativistic Kepler problem with\nThomas precession, whose treatment sheds some light on the amazing success of\nSommerfeld\u0027s theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1--91].",
    "arxiv_id": "quant-ph/0212082",
    "authors": [
      "Stefan Keppeler"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "nlin.CD"
    ],
    "doi": "10.1016/S0003-4916(03)00007-1",
    "journal_ref": "Ann. Phys. (NY) 304 (2003) 40-71",
    "title": "Semiclassical quantisation rules for the Dirac and Pauli equations",
    "url": "https://arxiv.org/abs/quant-ph/0212082"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "23ac46f0-2954-488d-bb3d-1d6e71d56926",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}