dorsal/arxiv
View SchemaOn the stochastic mechanics of the free relativistic particle
| Authors | Michele Pavon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108139 |
| URL | https://arxiv.org/abs/quant-ph/0108139 |
| DOI | 10.1063/1.1401135 |
| Journal | Journal of Mathematical Physics, 42 (2001), 4846-4856 |
Abstract
Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an $\M^4$-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation.
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"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"
},
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