Steady state, displacement current and spin polarization for massless fermion in a shear flow

TL;DR

This paper investigates spin polarization of massless fermions in shear flow, identifying the role of displacement current and its effects on magnetization, with comprehensive inclusion of scattering processes in a QED plasma.

Contribution

It explicitly determines the displacement current contribution in steady state shear flow, incorporating additional scattering processes and considering fermions as part of the medium.

Findings

Displacement current enhances magnetization at small and large momenta.

Displacement current suppresses magnetization at intermediate momenta.

Fermions reach the same steady state as the medium, including Compton scattering and pair annihilation.

Abstract

We consider spin polarization of massless fermions in a shear flow, whose complete contributions contain magnetization current and side-jump current known from collisional chiral kinetic theory. We argue that the side-jump current adopts interpretation of displacement current. We explicitly determine the displacement current contribution in the steady state reached in shear flow for a QED plasma. We find the displacement contribution enhances the magnetization contribution at small and large momenta, but leads to a suppression effect at intermediate momenta. Major differences from previous studies on collisional effect are: (i) the fermions are in the same steady state as the medium rather than being probes; (ii) Compton scattering and pair annihilation are also included in addition to the Coulomb scattering considered before.