  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.
