{
  "annotation_id": "8198b3de-37fb-4ec0-88a5-d846fa25c1dd",
  "date_created": "2026-03-02T18:00:46.926000Z",
  "date_modified": "2026-03-02T18:00:46.926000Z",
  "file_hash": "19b55bcfa94c205c5d7edf18db14448d4db6e4e9385aecd6e9d44361577c7373",
  "private": false,
  "record": {
    "abstract": "It is demonstrated how the right hand sides of the Lorentz Transformation\nequations may be written, in a Lorentz invariant manner, as 4--vector scalar\nproducts. The formalism is shown to provide a short derivation, in which the\n4--vector electromagnetic potential plays a crucial role, of the Lorentz force\nlaw of classical electrodynamics, and the conventional definition of the\nmagnetic field in terms spatial derivatives of the 4--vector potential. The\ntime component of the relativistic generalisation of the Lorentz force law is\ndiscussed. An important physical distinction between the space-time and\nenergy-momentum 4--vectors is also pointed out.",
    "arxiv_id": "physics/0307133",
    "authors": [
      "J. H. Field"
    ],
    "categories": [
      "physics.class-ph",
      "physics.ed-ph"
    ],
    "title": "Derivation of the Lorentz Force Law and the Magnetic Field Concept using   an Invariant Formulation of the Lorentz Transformation",
    "url": "https://arxiv.org/abs/physics/0307133"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bf9dc03f-4c29-4a54-b816-80eeef757d99",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}