{
  "annotation_id": "56e9ebcc-1752-4319-83a8-19e594b603a5",
  "date_created": "2026-03-02T18:01:45.131000Z",
  "date_modified": "2026-03-02T18:01:45.131000Z",
  "file_hash": "a2bfadecaf12da0c724a4d3f762dac2098a422412d67dd49ee11a750722f8585",
  "private": false,
  "record": {
    "abstract": "Given a positive energy solution of the Klein-Gordon equation, the motion of\nthe free, spinless, relativistic particle is described in a fixed Lorentz frame\nby a Markov diffusion process with non-constant diffusion coefficient. Proper\ntime is an increasing stochastic process and we derive a probabilistic\ngeneralization of the equation $(d\\tau)^2=-\\frac{1}{c^2}dX_{\\nu}dX_{\\nu}$. A\nrandom time-change transformation provides the bridge between the $t$ and the\n$\\tau$ domain. In the $\\tau$ domain, we obtain an $\\M^4$-valued Markov process\nwith singular and constant diffusion coefficient. The square modulus of the\nKlein-Gordon solution is an invariant, non integrable density for this Markov\nprocess. It satisfies a relativistically covariant continuity equation.",
    "arxiv_id": "quant-ph/0108139",
    "authors": [
      "Michele Pavon"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1401135",
    "journal_ref": "Journal of Mathematical Physics, 42 (2001), 4846-4856",
    "title": "On the stochastic mechanics of the free relativistic particle",
    "url": "https://arxiv.org/abs/quant-ph/0108139"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8ba75820-abbc-43ef-9dec-c83157873389",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}