Zeta Function Regularization of Infrared Divergences in Bose-Einstein Condensation

TL;DR

This paper reviews a perturbative approach using zeta function regularization to analyze infrared divergences in Bose-Einstein condensation, showing that dynamic modes do not shift the condensation temperature when two-loop effects are included.

Contribution

It introduces a reliable high-temperature expansion algorithm with zeta function regularization for calculating fluctuation effects in Bose gases, correcting previous one-loop results.

Findings

Dynamic modes do not alter the condensation temperature at two-loop order.

The regularization method accurately reproduces known results.

Two-loop contributions are essential for correct predictions.

Abstract

The perturbative calculation of the effect of fluctuations in the nonzero frequency modes of a weakly interacting Bose gas on the condensation temperature is reviewed. These dynamic modes, discarded in most of the recent studies, have a temperature-induced energy gap that allows for a perturbative approach. The simple, yet powerful algorithm used to calculate the effect in a high-temperature expansion in conjunction with zeta function regularization of infrared divergences is explained in detail. The algorithm is shown to be reliable by demonstrating that it reproduces known results for a series of examples. With two-loop contributions properly included, the dynamic modes are seen not to lead to a shift in the condensation temperature, thus revising our earlier finding obtained at one loop.