Invariance of the relativistic one-particle distribution function

TL;DR

This paper critically reviews the Lorentz invariance of the relativistic one-particle distribution function, emphasizing its fundamental role in relativistic statistical physics and clarifying existing treatments.

Contribution

It provides a comprehensive critique and clarification of the standard literature on the Lorentz invariance of the relativistic distribution function.

Findings

Highlights the importance of Lorentz invariance in relativistic distribution functions

Identifies gaps and inconsistencies in existing treatments

Proposes clarifications to standard approaches

Abstract

The one-particle distribution function is of importance both in non-relativistic and relativistic statistical physics. In the relativistic framework, Lorentz invariance is possibly its most fundamental property. The present article on the subject is a contrastive one: we review, discuss critically, and, when necessary, complete, the treatments found in the standard literature.