Abstract
We use linear response techniques to develop the previously proposed relativistic ideal fluid limit with a non-negligible spin density. We confirm previous results and obtain expressions for the microscopic transport coefficients using Kubo-like formulae and buld up the effective field theory from the computed correlation functions. We also confirm that polarization makes vortices aquire an effective mass via a mechanism similar to the Anderson-Higgs mechanism in superconductors. As speculated earlier, this could stabilize the ideal hydrodynamic limit against fluctuation-driven vortices
Highlights
An interesting problem in relativistic fluid dynamics is the inclusion of a nonzero polarization density within the fluid
We do not know what the system looks like microscopically but we know that its dynamics is “strongly coupled and high temperature enough” that the system quickly adjusts itself to local equilibrium after perturbed
We should reiterate that the results here come exclusively from “bottom-up” reasoning, independently from the microscopic theory: We assume we are close to local equilibrium, and use gradient expansions, causality, and unitarity analysis for derivation, together with the results of [1,2,3]
Summary
An interesting problem in relativistic fluid dynamics is the inclusion of a nonzero polarization density within the fluid. We should reiterate that the results here come exclusively from “bottom-up” reasoning, independently from the microscopic theory: We assume we are close to local equilibrium, and use gradient expansions, causality, and unitarity analysis for derivation, together with the results of [1,2,3]. This is in contrast with most approaches [4,5,6,7,11] which rely on a “top-down” microscopic description, usually using extensions of the Boltzmann equation. We shall proceed with a bottom-up linear response analysis, but keep in mind the microscopic results for further work
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