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arXiv · 1707.01388

Wigner functions of massive fermions in strong magnetic fields

Xin-li Sheng·Dirk H. Rischke·David Vasak·Qun Wang
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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 $\mu$ and $\mu_5$, 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.

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Xin-li Sheng, Dirk H. Rischke, David Vasak, Qun Wang. 2017-07-05. Wigner functions of massive fermions in strong magnetic fields. https://doi.org/10.1140/epja/i2018-12414-9

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