Relativistic diffusion of particles with a continuous mass spectrum

TL;DR

This paper develops a framework for relativistic diffusion processes with a continuous mass spectrum, focusing on Lorentz covariance, particle dynamics in electromagnetic fields, and the statistical mechanics of such gases.

Contribution

It introduces Lorentz covariant diffusion generators and analyzes the statistical mechanics and viscosity of relativistic diffusing particle gases.

Findings

Positivity conditions for relativistic diffusion generators

Construction of Lorentz covariant diffusions from random vector fields

Analysis of viscosity in a relativistic particle gas

Abstract

We discuss general positivity conditions necessary for a definition of a relativistic diffusion on the phase space. We show that Lorentz covariant random vector fields on the forward cone $p^{2}\geq 0$ lead to a definition of a generator of Lorentz covariant diffusions. We discuss in more detail diffusions arising from particle dynamics in a random electromagnetic field approximating the quantum field at finite temperature. We develop statistical mechanics of a gas of diffusing particles. We discuss viscosity of such a gas in an expansion in gradients of the fluid velocity.