{
  "annotation_id": "417b6c76-0f7f-4db4-ad8b-b9dfc80e9d6d",
  "date_created": "2026-03-02T18:00:53.500000Z",
  "date_modified": "2026-03-02T18:00:53.500000Z",
  "file_hash": "8f7c97de55f247a73cdd3bce1e719da56e897dd0e09e3472aec27a6d95b0f39d",
  "private": false,
  "record": {
    "abstract": "The Dirac particle, i.e. the dynamic system S_D, described by the free Dirac\nequation is investigated. Although the Dirac equation is written usually in the\nrelativistically covariant form, the dynamic system S_D is not completely\nrelativistic, because its description contains such absolute objects as $\\gamma\n$-matrices $\\gamma ^{k}$, forming a matrix vector. By means of the proper\nchange of variables the $\\gamma $-matrices are eliminated, but instead of them\nthe constant timlike vector $f^{k}$ appears. The vector $f^{k}$ describes an\nabsolute splitting of the space-time into space and time, which is\ncharacteristic for the nonrelativistic description. To investigate a degree of\nthe violation of the S_D relativistic description, we consider the classical\nDirac particle S_{Dcl}, obtained from S_D by means of the relativistic dynamic\ndisquantization. The classical dynamic system S_{Dcl} appears to be composite,\nbecause it has ten degrees of freedom. Six translational degrees of freedom are\ndescribed relativistically (without a reference to $f^{k}$), whereas four\ninternal degrees of freedom are described nonrelativistically, because their\ndescription refers to $f^{k}$. Coupling the absolute vector $f^{k}$ with the\nenergy-momentum vector of S_{Dcl}, the classical Dirac particle S_{Dcl} is\nmodified minimally. The vector $f^{k}$ ceases to be absolute, and the modified\nclassical Dirac particle S_{mDcl} becomes to be completely relativistic. The\ndynamic equations for S_{mDcl} are solved. Solutions for S_{Dcl} and S_{mDcl}\nare compared.",
    "arxiv_id": "physics/0412032",
    "authors": [
      "Yuri A. Rylov"
    ],
    "categories": [
      "physics.gen-ph"
    ],
    "title": "Is the Dirac particle completely relativistic?",
    "url": "https://arxiv.org/abs/physics/0412032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "503bbf3b-c713-47e5-9008-1a2b1849b15a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}