  By using the exact solutions of the Weyl equation in a constant magnetic
field, the equal-time Wigner function for magnetized chiral plasma is derived.
It is found that the dependence of the Wigner function on the component of
momentum along the magnetic field is asymmetric and is correlated with the
fermion chirality. Such a dependence is principal for reproducing the correct
chiral magnetic and chiral separation effects. In the lowest Landau level
approximation, the equation for the equal-time Wigner function in a strong
magnetic field is derived. By making use of this equation, it is found that the
longitudinal collective modes in a strong magnetic field are gapped plasmons
whose gap is determined by the magnetic field. Unlike the ordinary magnetic
field, an axial one allows for the dispersion law of the collective excitations
asymmetric in the wave vector. The thermoelectric phenomena for chiral fermions
in strong magnetic and axial magnetic fields are studied and the corresponding
transport coefficients are calculated.
