The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

Abstract:

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process is studied in an arbitrary inertial reference frame. In particular, we derive directly from the stochastic equations of motion in an arbitrary inertial frame the transport equation for the distribution function of the diffusing particles in phase-space. We explain why this result is not trivial and has, at the very least, methodological interest. We also show that this result offers a conceptually new proof of the well-known fact that the relativistic one-particle distribution function in phase-space is a Lorentz scalar.