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

Understand

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 $\mu_A \ne 0$.