Euler-Heisenberg Lagrangian under an axial gauge field

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 as spectral sum, of augmented Dirac operator: one with magnetic field chiral chemical potential, other electric spatial gauge, which resembles emergent vorticity. An enhancement Schwinger pair production is found for latter, more fully analyzed using worldline instanton formalism. There it overall due serving negative mass shift. Finally, we remark on exactly solvable massless case arbitrary gauges.