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

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.

Automated summary

By utilizing the second law of local thermodynamics and the first-order Palatini formalism, this study formulates relativistic spin hydrodynamics for quantum field theories with Dirac fermions in a curved torsionful background. The model treats spin density as an independent degree of freedom in an extended hydrodynamic description, with only three non-hydrodynamic modes corresponding to a spin vector. Linear response theory is used to observe mode mixing phenomena between transverse shear and spin density modes, with proposed field-theoretical methods to compute spin relaxation time and rotational viscosity.