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
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.
© SIF, Springer-Verlag GmbH Germany, part of Springer Nature, 2018