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

TL;DR

This paper derives second-order Wigner equations at global equilibrium considering space-time dependent electromagnetic fields, revealing new contributions to charge currents, energy-momentum tensor, and spin polarization, with tighter constraints on solutions.

Contribution

It introduces second-order corrections to Wigner functions and spin polarization due to space-time dependent electromagnetic fields, extending previous models.

Findings

New second-order contributions to charge currents and energy-momentum tensor.

Corrections to spin polarization pseudo-vector from electromagnetic fields.

Tighter constraints on Wigner function solutions with space-time dependent fields.

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.