  It is revealed that in dense relativistic matter in a magnetic field, there
exists a contribution to the axial current associated with a relative shift of
the longitudinal momenta in the dispersion relations of opposite chirality
fermions. Unlike the topological contribution in the axial current at the
lowest Landau level, recently discussed in the literature, the dynamical one
appears only in interacting matter and affects the fermions in all Landau
levels, including those around the Fermi surface. The induced axial current and
the shift of the Fermi surfaces of the left-handed and right-handed fermions
are expected to play an important role in transport and emission properties of
matter in various types of compact stars as well as in heavy ion collisions.
