The microcanonical ensemble of the ideal relativistic quantum gas with angular momentum conservation

TL;DR

This paper derives a comprehensive microcanonical partition function for an ideal relativistic quantum gas with fixed angular momentum and parity, using a group theoretical approach that fully accounts for particle spin without large volume approximations.

Contribution

It introduces a novel group theoretical method to compute the microcanonical partition function for relativistic quantum gases with angular momentum and parity conservation, extending previous results.

Findings

Provides explicit formulas for the microcanonical partition function at fixed multiplicities.

Extends existing literature by including particle spin and parity without large volume assumptions.

Connects the quantum and classical limits of the partition function.

Abstract

We derive the microcanonical partition function of the ideal relativistic quantum gas with fixed intrinsic angular momentum as an expansion over fixed multiplicities. We developed a group theoretical approach by generalizing known projection techniques to the Poincare' group. Our calculation is carried out in a quantum field framework and applies to particles with any spin. It extends known results in literature in that it does not introduce any large volume approximation and it takes particle spin fully into account. We provide expressions of the microcanonical partition function at fixed multiplicities in the limiting classical case of large volumes and large angular momenta and in the grand-canonical ensemble. We also derive the microcanonical partition function of the ideal relativistic quantum gas with fixed parity.