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.
Highlights
Quantum statistical density operators [33,34,35,36,37]
The true novelty of spin hydrodynamics in this regime is two-fold [13]: 1) the spin, or equivalently the fluid vorticity, affects the local thermodynamic laws used in hydrodynamics, as a second order gradient correction to the first law of thermodynamics, 2) the energy-momentum tensor has an anti-symmetric part which is proportional to the rate of change of the spin tensor, 1We note that the term “local equilibrium” has been used in literature in different contexts
We addressed several theoretical issues in relativistic hydrodynamics with spin polarization
Summary
We review the definition of the energy-momentum tensor and the spin current from the viewpoint of the first-order (or Palatini) formalism for background spacetime [49]. We consider quantum field theory (QFT) in a torsionful (Einstein-Cartan) background geometry [50] and introduce currents and the Ward-Takahashi identities [51, 52] associated with diffeomorphism, local Lorentz invariance and flavor symmetry
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