Coordinates in the relativistic Boltzmann theory

TL;DR

This paper introduces new coordinate systems for representing the relativistic Boltzmann collision operator, clarifying known and novel representations, and demonstrating their utility in solving open problems in the field.

Contribution

The paper derives and compares various coordinate systems for the relativistic Boltzmann operator, including some newly proposed ones, aiding in mathematical analysis and problem-solving.

Findings

Established equivalence between known and new representations.

Identified a new coordinate system used to solve open problems.

Enhanced understanding of the structure of the relativistic Boltzmann operator.

Abstract

It is often the case in mathematical analysis that solving an open problem can be facilitated by finding a new set of coordinates which may illumniate the known difficulties. In this article, we illustrate how to derive an assortment coordinates in which to represent the relativistic Boltzmann collision operator. We show the equivalence between some known representations, and others which seem to be new. One of these representations has been used recently to solve several open problems.