An Exact QED_{3+1} Effective Action

TL;DR

This paper derives an exact expression for the QED_{3+1} effective action in static, spatially varying magnetic fields, and confirms the validity of the derivative expansion through asymptotic analysis.

Contribution

It provides the first exact calculation of the QED_{3+1} effective action for inhomogeneous magnetic fields and verifies the derivative expansion against independent methods.

Findings

Exact effective action computed for inhomogeneous magnetic fields.

Asymptotic expansion matches independent derivative expansion results.

Generalizes previous QED_{2+1} findings to 3+1 dimensions.

Abstract

We compute the exact QED_{3+1} effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. An asymptotic expansion of this exact effective action yields an all-orders derivative expansion, the first terms of which agree with independent derivative expansion computations. These results generalize analogous earlier results by Cangemi et al in QED_{2+1}.