Critical Behavior of a Relativistic Bose Gas

TL;DR

This paper provides an exact analytical description of the thermodynamic and critical behavior of a relativistic ideal Bose gas across all regimes, confirming previous numerical findings and deriving a comprehensive energy density expression.

Contribution

It introduces exact analytical formulas for the thermodynamics and critical behavior of a relativistic Bose gas, extending previous numerical studies.

Findings

Analytical critical behavior matches numerical results.

Derived a closed-form expression for energy density.

Unified description valid in all regimes.

Abstract

We show that the thermodynamic behavior of relativistic ideal Bose gas, recently studied numerically by Grether et al., can be obtained analytically. Using the analytical results, we obtain the critical behavior of the relativistic Bose gas exactly for all the regimes. We show that these analytical results reduce to those of Grether et al. in different regimes of the Bose gas. Furthermore, we also obtain an analytically closed form expression for the energy density for the Bose gas which is valid in all regimes.