Corrections from spacetime dependent electromagnetic fields to Wigner functions and spin polarization

We have derived the Wigner equations at global equilibrium with constant vorticity but spacetime dependent electromagnetic fields up to second order in a 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 pesudovector from both constant and varying electromagnetic fields. We also find that the spacetime dependent electromagnetic field provides a tighter constraint on the solutions of Wigner functions in global equilibrium compared with a constant electromagnetic field.