Consistent regularization and renormalization in models with inhomogeneous phases

TL;DR

This paper discusses methods for regularizing and renormalizing quantum fluctuations in models with inhomogeneous phases, applying these techniques to specific models in condensed matter and high-energy physics to ensure consistent calculations of vacuum energy.

Contribution

It introduces and compares regularization and renormalization schemes for quantum fluctuations in inhomogeneous phases, with applications to NJL and quark-meson models.

Findings

Consistent regularization schemes yield finite vacuum energies.

Application to NJL and quark-meson models demonstrates the methods.

Comparison of energy cutoff and dimensional regularization approaches.

Abstract

In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different consistent ways of regularizing and renormalizing quantum fluctuations, focusing on a symmetric energy cutoff scheme and dimensional regularization. We apply these techniques calculating the vacuum energy in the NJL model in 1+1 dimensions in the large-$N_c$ limit and the 3+1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.