  We assess the applicability of the Wigner function formulation in its present
form to the chiral Magnetic Effect and noted some issues regarding the
conservation and the consistency of the electric current in the presence of an
inhomogeneous and time dependent axial chemical potential. The problems are
rooted in the ultraviolet divergence of the underlying field theory associated
with the axial anomaly and can be fixed with the Pauli-Villars regularization
of the Wigner function.
