{
  "annotation_id": "f1b7693d-3055-4937-aece-8d2b7da392c3",
  "date_created": "2026-03-02T18:01:49.495000Z",
  "date_modified": "2026-03-02T18:01:49.495000Z",
  "file_hash": "b87f71efd670569377c2f9ef0437db595a0cfdc5c7d9ca128c9722230779723c",
  "private": false,
  "record": {
    "abstract": "In contrast to formulations of the Dirac theory by Hestenes and by the\ncurrent author, the formulation recently presented by W. P. Joyce [J. Phys. A:\nMath. Gen. 34 (2001) 1991--2005] is equivalent to the usual Dirac equation only\nin the case of vanishing mass. For nonzero mass, solutions to Joyce\u0027s equation\ncan be solutions either of the Dirac equation in the Hestenes form or of the\nsame equation with the sign of the mass reversed, and in general they are\nmixtures of the two possibilities. Because of this relationship, Joyce obtains\ntwice as many linearly independent plane-wave solutions for a given momentum\neigenvalue as exist in the conventional theory. A misconception about the\nsymmetry of the Hestenes equation and the geometric significance of the\nalgebraic spinors is also briefly discussed.",
    "arxiv_id": "quant-ph/0202060",
    "authors": [
      "William E. Baylis"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/35/22/401",
    "title": "Comments on \"Dirac theory in spacetime algebra\"",
    "url": "https://arxiv.org/abs/quant-ph/0202060"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d6ef797c-d0ee-4432-b740-af5dd4d0393d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}