Thermodynamic equilibrium of massless fermions with vorticity, chirality and electromagnetic field

TL;DR

This paper investigates the thermodynamics of massless Dirac fermions at equilibrium, focusing on the effects of vorticity, chirality, and electromagnetic fields, revealing that certain chiral effects are unaffected by uniform electromagnetic fields.

Contribution

It provides a non-perturbative analysis of axial charge and electromagnetic field effects on massless fermions, including exact solutions of the Dirac equation in a thermodynamic context.

Findings

Chiral vortical and axial vortical effects are unaffected by homogeneous electromagnetic fields.

Exact solutions of the Dirac equation are used to incorporate electromagnetic effects non-perturbatively.

Thermal expectation values are computed with a perturbative expansion in thermal vorticity.

Abstract

We present a study of the thermodynamics of the massless free Dirac field at equilibrium with axial charge, angular momentum and and external electromagnetic field to assess the interplay between chirality, vorticity and electromagnetic field in relativistic fluids. After discussing the general features of global thermodynamic equilibrium in quantum relativistic statistical mechanics, we calculate the thermal expectation values. Axial imbalance and electromagnetic field are included non-perturbatively by using the exact solutions of the Dirac equation, while a perturbative expansion is carried out in thermal vorticity. It is shown that the chiral vortical effect and the axial vortical effect are not affected by a constant homogeneous electromagnetic field.