{
  "abstract": "We investigate the non-relativistic limit of the generalized Dirac equation in a weak, static, and spherically symmetric background of symmetric teleparallel gravity. The underlying generalized spinor connection incorporates the complete Clifford-algebra basis and introduces additional couplings to the non-metricity sector beyond those of the conventional Dirac theory. Working in the coincident gauge and adopting the weak-field Schwarzschild geometry in isotropic coordinates, we derive the corresponding generalized Dirac Hamiltonian and perform successive Foldy--Wouthuysen transformations up to order $1/m^2$, retaining terms to first order in the gravitational potential and its spatial derivatives. The resulting block-diagonal Hamiltonian contains not only the expected gravitational counterparts of the kinetic, spin--orbit, and Darwin interactions, but also additional operator structures generated by the generalized spinor connection. In particular, direct spin--gravity, anisotropic spin--momentum--gravity, and tidal spin--momentum couplings arise naturally from the generalized metric-affine interaction. We further perform an order-of-magnitude analysis for an electron in the Earth's weak gravitational field to justify the adopted truncation of the inverse-mass expansion. These results demonstrate that the generalized Dirac equation in a symmetric teleparallel background gives rise to new low-energy interaction channels involving the fermion spin, momentum, and spatial derivatives of the gravitational field. The resulting effective Hamiltonian provides a framework for exploring phenomenological constraints on the additional couplings entering the generalized spinor connection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Class. Quantum Grav. 43 (2026) 205016",
  "arxiv": "2607.27889",
  "author_total": 4,
  "authors": [
    {
      "name": "Sabutay Ugur"
    },
    {
      "name": "Muzaffer Adak"
    },
    {
      "name": "Ali Bagci"
    },
    {
      "name": "Caglar Pala"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3xyx4kymn13j9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.27889",
  "fulltext_url": null,
  "id": "3xyx4kymn13j9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.27889",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.27889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3xyx4kymn13j9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2607.27889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.27889"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Foldy--Wouthuysen Transformation of the Generalized Dirac Equation in Symmetric Teleparallel Gravity",
  "title_text": "Foldy--Wouthuysen Transformation of the Generalized Dirac Equation in Symmetric Teleparallel Gravity",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/3xyx4kymn13j9",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/1361-6382/aeb21e",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}