Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

TL;DR

This paper develops a relativistic spin hydrodynamics framework incorporating torsion for quantum field theories with Dirac fermions, introducing a new transport coefficient and analyzing spin relaxation and mode mixing.

Contribution

It formulates a novel relativistic spin hydrodynamics theory with torsion, identifying a new rotational viscosity and exploring linear response and spin relaxation mechanisms.

Findings

Identification of a new transport coefficient: rotational viscosity.

Observation of mode mixing between shear and spin density modes.

Proposals for computing spin relaxation time via Green-Kubo formulas.

Abstract

Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.