Brownian motion approach to the ideal gas of relativistic particles

Abstract

The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal corrections, to the both relaxation times $T$ (of stationary autocorrelations) and transient relaxation time of momentum, appear slowing down the processes. The transient relaxation time of the velocity does not depend {\it explicitly} on temperature, $T(v_0)= m(v_0)/γ\equiv ε_0/γc^2$, and it is proportional to the initial energy of a relativistic Brownian particle.