Corrections from space-time dependent electromagnetic fields to Wigner functions and spin polarization

Abstract

We have derived the Wigner equations at global equilibrium with constant vorticity but space-time dependent electromagnetic fields up to second order in semiclassical expansion. We obtain the new second-order contributions to the charge currents and energy-momentum tensor from the varying electromagnetic fields. We also compute the new corrections to the spin polarization pesudo-vector from both contant and varying electromagnetic fields. We also find that the space-time dependent electromagnetic field provides a tighter constraint on the solutions of Wigner functions in global equilibrium compared with constant electromagnetic field.