Wigner functions of massive fermions in strong magnetic fields

Abstract

We compute the covariant Wigner function for spin-1/2 fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature $T$ and non-zero fermion-number and chiral-charge chemical potentials $μ$ and $μ_5$, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

RevTex 4, 15 pages, 2 figures; discussions about the degeneracy of the eigen-energy from p_x are added; to appear in EPJA