Causality and dissipation in relativistic polarizable fluids

Abstract

Using field theory techniques we analyze the perfect fluid limit, defined as fastest possible local equilibration, in a medium with polarizability, defined as a nonzero local equilibrium partition of angular momentum into spin and vorticity. We show that to restore causality a relaxation term linking vorticity and polarization, analogous to the Israel-Stewart term linking viscous forces and gradients, is required. This term provides the minimum amount of dissipation a locally thermalized relativistic medium with polarizability must have, independently of its underlying degrees of freedom. For materials susceptible to spin alignment an infrared acausal mode remains, which we interpret as a Banks-Casher mode signaling spontaneous transition to a polarized phase. With these ingredients, we propose a candidate for a fully causal Lagrangian of a relativistic polarizable system near the perfect fluid limit, and close with some phenomenological considerations.