The axial charge relaxation coefficient in the Schwinger-Keldysh effective theory of QCD must be of second order in the quark mass, Γ_A = γ_A m_q^2, subleading in the broken phase and leading in the restored phase.
Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method
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We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics.We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.
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Schwinger-Keldysh effective action for hydrodynamics with approximate symmetries
The axial charge relaxation coefficient in the Schwinger-Keldysh effective theory of QCD must be of second order in the quark mass, Γ_A = γ_A m_q^2, subleading in the broken phase and leading in the restored phase.