Abstract
We study Wigner equations for massless spin-$1/2$ charged fermions at global equilibrium in static and uniform vorticity and electromagnetic fields. The Wigner functions can be solved order by order from Wigner equations through the power expansion of the vorticity and electromagnetic fields. The nondissipative charge currents and the stress tensor up to the second order can be obtained from Wigner functions. The charge and energy densities and the pressure have contributions from vorticity and electromagnetic fields at the second order. The vector and axial Hall currents can be induced along the direction orthogonal to vorticity and electromagnetic fields at the second order. We also find that the trace anomaly emerges naturally in renormalization of the stress tensor by including quantum corrections from electromagnetic fields.
Highlights
It is well known in classical electrodynamics that the electromagnetic field can generate electric currents, such as Olm’s current from electric fields or Hall’s current from magnetic fields
The nondissipative charge currents and the stress tensor up to the second order can be obtained from Wigner functions
We find that the trace anomaly emerges naturally in renormalization of the stress tensor by including quantum corrections from electromagnetic fields
Summary
It is well known in classical electrodynamics that the electromagnetic field can generate electric currents, such as Olm’s current from electric fields or Hall’s current from magnetic fields. In addition to CME and CVE, chiral currents can be generated by vorticity and magnetic fields, these are called the chiral separate effect (CSE) [8,9] or the local polarization effect (LPE) [10]. Theoretical studies of these effects have been carried. IV and V, we present the induced vector and axial currents and energy-momentum tensor up to the second order. The electric charge of the fermion is absorbed into the vector potential Aμ
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