Relativistic Bose gases at finite density

TL;DR

This paper analyzes a relativistic Bose gas at finite density, calculating thermodynamic properties at zero and finite temperatures, and determining the critical temperature for Bose-Einstein condensation using perturbative and nonperturbative methods.

Contribution

It provides a comprehensive calculation of thermodynamic quantities and the critical temperature for relativistic Bose gases, combining perturbative, effective field theory, and Monte Carlo methods.

Findings

Calculated pressure, charge density, and speed of sound at zero temperature.

Derived the critical temperature for Bose-Einstein condensation for N=2.

Connected relativistic and nonrelativistic Bose gas results.

Abstract

We consider a massive relativistic Bose gas with $N$ complex scalars at finite density. At zero temperature, we calculate the pressure, charge density and the speed of sound in the one-loop approximation. In the nonrelativistic limit, we obtain the classic results for the dilute Bose gas. We also discuss finite-temperature effects. In particular, we consider the problem of calculating the critical temperature for Bose-Einstein condensation. Dimensional reduction and effective-field-theory methods are used to perturbatively calculate the effects of the nonstatic Matsubara modes. Calculations of $T_c$ in the effective 3d theory require nonperturbative methods. Using the Monte Carlo simulations of X. Sun [Phys. Rev. {\bf E67}, 066702 (2003)] and the seven-loop variational perturbation theory (VPT) calculations of B. Kastening [Phys. Rev. {\bf A70}, 043621 (2004)], we obtain $T_c$ for N=2 to second order in the interaction.