General thermodynamic equilibrium with axial chemical potential for the free Dirac field

TL;DR

This paper derives the constitutive equations for a free massless Dirac field at thermodynamic equilibrium with acceleration, rotation, and axial chemical potential, revealing effects relevant to chiral hydrodynamics.

Contribution

It provides a second-order expansion of stress-energy tensor and currents with finite axial chemical potential, expressing coefficients as correlators of angular momenta and boost operators.

Findings

Axial chemical potential induces non-zero stress-energy tensor components at first order in vorticity.

The expansion coefficients are explicitly expressed as correlators of angular momenta and boost operators.

Results confirm the breaking of parity invariance due to axial chemical potential.

Abstract

We calculate the constitutive equations of the stress-energy tensor and the currents of the free massless Dirac field at thermodynamic equilibrium with acceleration and rotation and a conserved axial charge by using the density operator approach. We carry out an expansion in thermal vorticity to the second order with finite axial chemical potential $\mu_A$. The obtained coefficients of the expansion are expressed as correlators of angular momenta and boost operators with the currents. We confirm previous observations that the axial chemical potential induces non-vanishing components of the stress-energy tensor at first order in thermal vorticity due to breaking of parity invariance of the density operator with $\mu_A \ne 0$. The appearance of these components might play an important role in chiral hydrodynamics.