The epsilon-expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature

TL;DR

This paper applies the epsilon-expansion and momentum-shell renormalization group method to analyze the finite-temperature Bose gas, resolving previous discrepancies by properly handling infrared divergencies in both phases.

Contribution

It demonstrates that correct treatment of infrared divergencies using epsilon-expansion unifies the analysis of symmetric and symmetry-broken phases.

Findings

Infrared divergencies are crucial at finite temperature.

Proper epsilon-expansion yields identical universal properties in both phases.

Resolves previous discrepancies in Bose gas phase analysis.

Abstract

We discuss the application of the momentum-shell renormalization group method to the interacting homogeneous Bose gas in the symmetric and in the symmetry-broken phases. It is demonstrated that recently discussed discrepancies are artifacts of not taking proper care of infrared divergencies appearing at finite temperature. If these divergencies are taken into account and treated properly by means of the epsilon-expansion, the resulting renormalization group equations and the corresponding universal properties are identical in the symmetric and the symmetry-broken phases.