Spin Polarized Quasi-particle in Off-equilibrium Medium

Abstract

It is usually believed that physics in off-equilibrium state characterized by hydrodynamic gradient can be equivalently studied using equilibrium state with suitable metric perturbation. We scrutinize this assumption using chiral kinetic theory in curved space, focusing on spin response to hydrodynamic gradient. Two effects of metric perturbation have been identified: one is to change particle motion by scattering it off the metric fields, which does capture spin response to hydrodynamic gradient, but is limited by kinematic condition in the scattering picture. The other is the genuine effect of off-equilibrium state, which is realizable by mapping the equilibrium state in curved space to flat space through a suitable frame choice. It lifts the kinematic condition in the spin response to hydrodynamic gradient. We classify off-equilibrium effect on spin polarization into modifications of (i) spectral function; (ii) distribution function; (iii) KMS relation. While the last two have been studied using chiral kinetic theory, the first one is usually ignored in kinetic description. We perform a detailed analysis on the first one, finding the radiative correction to spectral function leads to a polarized quasi-particle. The degeneracy of spin responses to different hydrodynamic sources at tree-level is also lifted by radiative correction.