Eur. Phys. J. A (2018) 54: 21
https://doi.org/10.1140/epja/i2018-12414-9

Regular Article - Theoretical Physics

Wigner functions for fermions in strong magnetic fields

¹ Interdisciplinary Center for Theoretical Study and Department of Modern Physics, University of Science and Technology of China, 230026, Hefei, Anhui, China
² Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, D-60438, Frankfurt am Main, Germany
³ Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Str. 1, D-60438, Frankfurt am Main, Germany

^* e-mail: qunwang@ustc.edu.cn

Received: 5 July 2017
Accepted: 11 October 2017
Published online: 19 February 2018

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 and , 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.