Wigner function and kinetic phenomena for chiral plasma in a strong magnetic field

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.