{
  "annotation_id": "5360c4f1-6fd1-4ab7-a308-a482d67457e5",
  "date_created": "2026-03-02T18:02:06.878000Z",
  "date_modified": "2026-03-02T18:02:06.878000Z",
  "file_hash": "a45b207652a0b9d2824e04616e9794da11f231431dee5589cf6e720b438c51e4",
  "private": false,
  "record": {
    "abstract": "In this paper we construct an analytical separation (diagonalization) of the\nfull (minimal coupling) Dirac equation into particle and antiparticle\ncomponents. The diagonalization is analytic in that it is achieved without\ntransforming the wave functions, as is done by the Foldy-Wouthuysen method, and\nreveals the nonlocal time behavior of the particle-antiparticle relationship.\nWe interpret the zitterbewegung and the result that a velocity measurement (of\na Dirac particle) at any instant in time is, as reflections of the fact that\nthe Dirac equation makes a spatially extended particle appear as a point in the\npresent by forcing it to oscillate between the past and future at speed c. From\nthis we infer that, although the form of the Dirac equation serves to make\nspace and time appear on an equal footing mathematically, it is clear that they\nare still not on an equal footing from a physical point of view. On the other\nhand, the Foldy-Wouthuysen transformation, which connects the Dirac and square\nroot operator, is unitary. Reflection on these results suggests that a more\nrefined notion (than that of unitary equivalence) may be required for physical\nsystems.",
    "arxiv_id": "quant-ph/0405151",
    "authors": [
      "T. L. Gill",
      "W. W. Zachary"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/38/31/006",
    "title": "Analytic Representation of The Dirac Equation",
    "url": "https://arxiv.org/abs/quant-ph/0405151"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d6067773-ab86-43b6-8a2d-897ccdf1f53b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}