dorsal/arxiv
View SchemaThe tensor analytical relationships of Dirac's equation
| Authors | Cornelius Lanczos |
|---|---|
| Categories | |
| ArXiv ID | physics/0508002 |
| URL | https://arxiv.org/abs/physics/0508002 |
| Journal | Z.Phys. 57 (1929) 447-473 |
Abstract
Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and covariant [bilinear] constructions of Dirac's theory are developed uniformly and systematically. A method of obtaining a covariant formulation of the equations using customary tensor calculus also offers itself unequivocally if we duplicate the Dirac equations. (Editorial note: In this paper Lanczos introduces his ``fundamental equation,'' Eq. (54), from which two Dirac fields forming an isospin doublet, or two spin 1 fields of opposite parities, derive.)
{
"annotation_id": "5f2e5ffc-d1cf-4584-9fdd-963f2d5f0f56",
"date_created": "2026-03-02T18:01:00.475000Z",
"date_modified": "2026-03-02T18:01:00.475000Z",
"file_hash": "f5ffd4860501a44f3da1c801afe98245503fa9e1d61b599157684fe67edfefff",
"private": false,
"record": {
"abstract": "Dirac\u0027s equation of the electron will be discussed by using quaternions as\nthe basis of a new formalism which seems to be very well adapted to the\nproblem. The transformation properties of the equations as well as the\ninvariant and covariant [bilinear] constructions of Dirac\u0027s theory are\ndeveloped uniformly and systematically. A method of obtaining a covariant\nformulation of the equations using customary tensor calculus also offers itself\nunequivocally if we duplicate the Dirac equations. (Editorial note: In this\npaper Lanczos introduces his ``fundamental equation,\u0027\u0027 Eq. (54), from which two\nDirac fields forming an isospin doublet, or two spin 1 fields of opposite\nparities, derive.)",
"arxiv_id": "physics/0508002",
"authors": [
"Cornelius Lanczos"
],
"categories": [
"physics.hist-ph"
],
"journal_ref": "Z.Phys. 57 (1929) 447-473",
"title": "The tensor analytical relationships of Dirac\u0027s equation",
"url": "https://arxiv.org/abs/physics/0508002"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "3c54be64-e33d-4b36-9956-ed50f5c4db58",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}