  The chiral anomaly is one of the robust quantum effects in relativistic field
theories with a chiral symmetry where charges in chiral sectors appear to be
separately conserved. The chiral anomaly, which is often associated with a
renormalization-invariant topological term, is a violation of this conservation
law due to quantum effects. Such anomalies manifest in Weyl materials as an
electromagnetic field-induced transfer of charge between Fermi pockets.
However, the emergent nature of the conservation of chiral charge leads to
manifestations of the chiral anomaly response that depend on the details of the
system such as the strength of interactions. In this paper, we apply an
approach where the chiral symmetry in solid materials is replaced by the
combination of charge $U(1)$ gauge and spatial translation symmetry. The chiral
anomaly in this case is replaced by a mixed anomaly between the two symmetries
and the chiral charge can be defined as being proportional to the total
momentum. We show that the chiral anomaly associated with this chiral charge is
unrenormalized by interactions in contrast to other chiral charges in $(1+1)D$
whose renormalization is regularization dependent. In $(3+1)$D Weyl systems,
this chiral anomaly is equivalent to the charge transferred between Fermi
surfaces which can be measured through changes in Fermi-surface-enclosed
volume. We propose a pump-probe technique to measure this.
