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

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.