Relativistic phase space: dimensional recurrences

TL;DR

This paper develops a method to relate phase space calculations across different dimensions by using geometric confinement and taking limits, resulting in recurrence relations expressed as mass integrals.

Contribution

It introduces a novel approach to derive dimensional recurrence relations for phase space expressions using geometric confinement and limit processes.

Findings

Derived explicit recurrence relations between phase space in different dimensions.

Connected phase space calculations to mass integrals involving extraneous momenta.

Provided a framework for systematic dimensional reduction and extension in phase space analysis.

Abstract

We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius $R$ and taking the limit as $R \to \infty$. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension.