{
  "annotation_id": "ceef753a-2730-4086-8be4-33c856de3ef4",
  "date_created": "2026-03-02T18:02:24.066000Z",
  "date_modified": "2026-03-02T18:02:24.066000Z",
  "file_hash": "11f24e265d7c42262efa74ae2e29ff69d00ab2e3811c54c4571b2d6e752b72ad",
  "private": false,
  "record": {
    "abstract": "A first-order relativistic wave equation is constructed in five dimensions.\nIts solutions are eight-component spinors, which are interpreted as\nsingle-particle fermion wave functions in four-dimensional spacetime. Use of a\n``cylinder condition\u0027\u0027 (the removal of explicit dependence on the fifth\ncoordinate) reduces each eight-component solution to a pair of degenerate\nfour-component spinors obeying the Dirac equation. This five-dimensional method\nis used to obtain solutions for a free particle and for a particle moving in\nthe Coulomb potential. It is shown that, under the cylinder condition, the\nresults are the same as those from the Dirac equation. Without the cylinder\ncondition, on the other hand, the equation predicts some interesting new\nphenomena. It implies the existence of a scalar potential, and for zero-mass\nparticles it leads to a four-dimensional fermionic equation analogous to\nMaxwell\u0027s equation with sources.",
    "arxiv_id": "quant-ph/0512140",
    "authors": [
      "N. Redington",
      "M. A. K. Lodhi"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-ph"
    ],
    "doi": "10.1063/1.2435983",
    "journal_ref": "J.Math.Phys.48:022303,2007",
    "title": "A Simple Five-Dimensional Wave Equation for a Dirac Particle",
    "url": "https://arxiv.org/abs/quant-ph/0512140"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d4b64710-f243-49c2-b22d-0d6daa2d85a4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}