The Two-Loop Euler-Heisenberg Lagrangian in Dimensional Renormalization

TL;DR

This paper resolves a discrepancy in the two-loop Euler-Heisenberg Lagrangian calculations by performing the computation using dimensional regularization, clarifying previous conflicting results.

Contribution

It introduces a dimensional regularization approach to compute the two-loop Euler-Heisenberg Lagrangian, addressing inconsistencies in prior proper-time regularization methods.

Findings

Discrepancy between previous calculations is resolved.

Dimensional regularization provides a consistent framework.

Clarifies the correct form of the two-loop Lagrangian.

Abstract

We clarify a discrepancy between two previous calculations of the two-loop QED Euler-Heisenberg Lagrangian, both performed in proper-time regularization, by calculating this quantity in dimensional regularization.