  Weyl semimetals realize massless relativistic fermions with two Weyl nodes
separated in energy and momentum space, whose low-energy physics is described
by Dirac fermions with an axial gauge constant. Here, we study their
electromagnetic linear responses based on the effective field theory and on the
chiral kinetic theory. Although the static chiral magnetic effect is canceled
by the Chern-Simons current under the Pauli-Villars regularization, a dynamical
magnetic field is found capable of driving an electric current along its
direction, with the total transported charge being independent of temperature
and chemical potential for a uniform field. We also incorporate dissipation in
the relaxation-time approximation and study collective excitations coupled with
Maxwell electromagnetic fields when Weyl node populations deviate from
equilibrium. Their dispersion relations at low frequency and long wavelength
are determined only by electric, chiral magnetic, and anomalous Hall
conductivities, which predict unstable modes leading to anisotropic generation
of electromagnetic waves oriented to the direction of Weyl node separation.
