Zeta Function Regularization of Infrared Divergences in Bose-Einstein Condensation
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.
Keywords
Cite
@article{arxiv.cond-mat/0301050,
title = {Zeta Function Regularization of Infrared Divergences in Bose-Einstein Condensation},
author = {Adriaan M. J. Schakel},
journal= {arXiv preprint arXiv:cond-mat/0301050},
year = {2007}
}
Comments
17 pages, no figures Updated version includes two-loop contributions