Euler-Heisenberg Lagrangian under an axial gauge field

TL;DR

This paper explores modifications to the Euler-Heisenberg Lagrangian in the presence of a constant axial gauge field, revealing exact solutions and an enhancement in pair production due to axial gauge effects.

Contribution

It provides exact eigendecompositions for specific configurations and analyzes the impact of axial gauge fields on quantum electrodynamics phenomena.

Findings

Exact eigendecomposition for magnetic field with chiral chemical potential.

Enhanced Schwinger pair production in electric field with axial gauge.

Axial gauge acts as a negative mass shift, increasing pair production.

Abstract

Augmentations to the Euler-Heisenberg Lagrangian (QED one-loop effective action in homogeneous electromagnetic fields) under a constant background axial gauge are examined. Two special configurations admit an exact eigendecomposition, and hence effective action as a spectral sum, of the augmented Dirac operator: one with a magnetic field with chiral chemical potential, and the other with an electric field with spatial axial gauge, which resembles an emergent vorticity. An enhancement to Schwinger pair production is found for the latter, which is more fully analyzed using the worldline instanton formalism. There it is found the overall enhancement is due to the spatial axial gauge serving as a negative mass shift. Finally, we remark on the exactly solvable massless case for arbitrary electromagnetic and axial gauges.