On the stochastic mechanics of the free relativistic particle

Michele Pavon

Research output: Contribution to journalArticlepeer-review


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 nonconstant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation (d τ)2 = - (1/c2)dXv dXv. A random time-change transformation provides the bridge between the t and the τ domain. In the τ domain, we obtain an double-struck M sign 4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, nonintegrable density for this Markov process. It satisfies a relativistically covariant continuity equation.

Original languageEnglish (US)
Pages (from-to)4846-4856
Number of pages11
JournalJournal of Mathematical Physics
Issue number10
StatePublished - Oct 2001

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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