Finite Temperature Description of an Interacting Bose Gas

TL;DR

This paper derives the equation of state for an interacting Bose gas at finite temperature using relativistic quantum field theory, incorporating thermal and quantum corrections, and connects it to superfluid and dark matter phenomenology.

Contribution

It introduces a relativistic quantum field theoretical framework for Bose gases at finite temperature, including a novel treatment of dual chemical potentials to resolve the Hohenberg-Martin dilemma.

Findings

Reproduces known non-relativistic results in the appropriate limit.

Provides a formalism applicable to Bose-Einstein condensates and superfluid dark matter.

Connects the formalism to hydrodynamical two-fluid models.

Abstract

We derive the equation of state of a Bose gas with contact interactions using relativistic quantum field theory. The calculation accounts for both thermal and quantum corrections up to 1-loop order. We work in the Hartree-Fock-Bogoliubov approximation and follow Yukalov's prescription of introducing two chemical potentials, one for the condensed phase and another one for the excited phase, to circumvent the well-known Hohenberg-Martin dilemma. As a check on the formalism, we take the non-relativistic limit and reproduce known non-relativistic results. Finally, we translate our results to the hydrodynamical, two-fluid model for finite-temperature superfluids. Our results are relevant for the phenomenology of Bose-Einstein Condensate and superfluid dark matter candidates, as well as the color-flavor locking phase of quark matter in neutron stars.