Relativistic problem of random flights and Nelson's stochastic mechanics

Daniela Dohrn, Francesco Guerra, Patrizta Ruggiero

Francesco Guerra

Eric A. Carlen

Thaddeus George Dankel

Yuri E. Gliklikh

Gian Fabrizio De Angelis

An extension of Nelson’s stochastic mechanics to the relativistic domain is proposed. To each pure state of a spinless relativistic quantum particle corresponds a Markov process t ]ξt, where the random variable ξt represents, at every time t, the space position of the particle in the sense of Newton and Wigner. The process t ]ξt is not a diffusion but the usual Nelson’s theory is restored in the nonrelativistic limit.