Second-order charge currents and stress tensor in a chiral system

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.