{
  "annotation_id": "53c02471-908a-4bfa-83e7-b1e5313d448e",
  "date_created": "2026-03-02T18:00:45.887000Z",
  "date_modified": "2026-03-02T18:00:45.887000Z",
  "file_hash": "e6953aaf710099bb00e48b236d8e67a37cc3b28f95ee176e068f0933bbe69910",
  "private": false,
  "record": {
    "abstract": "It is shown that for a relativistic particle moving in an electromagnetic\nfield its equations of motion written in a form of the second law of Newton can\nbe reduced with the help of elementary operations to the Hamilton-Jacobi\nequation. The derivation is based on a possibility of transforming the equation\nof motion to a completely antisymmetric form. Moreover, by perturbing the\nHamilton-Jacobi equation we obtain the principle of least action.\\\n  The analogous procedure is easily extended to a general relativistic motion\nof a charged relativistic particle in an electromagnetic field. It sis also\nshown that the special-relativistic Hamilton-Jacobi equation for a free\nparticle allows one to easily demonstrate the wave-particle duality inherent to\nthis equation and, in addition, to obtain the operators of the four-momentum\nwhose eigenvalues are the classical four-momentum",
    "arxiv_id": "physics/0309059",
    "authors": [
      "A. Granik"
    ],
    "categories": [
      "physics.gen-ph",
      "physics.ed-ph"
    ],
    "title": "On an Elementary Derivation of the Hamilton-Jacobi Equation from the   Second Law of Newton",
    "url": "https://arxiv.org/abs/physics/0309059"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "723a2f8b-379c-4ec8-896a-8711f27699e7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}