Three-loop Euler-Heisenberg Lagrangian and asymptotic analysis in 1+1 QED

TL;DR

This paper extends the analysis of the Euler-Heisenberg Lagrangian to three loops in 1+1 dimensional QED, exploring its asymptotic behavior and comparing it with worldline instanton predictions to shed light on photon amplitude growth.

Contribution

It provides the first three-loop calculation of the Euler-Heisenberg Lagrangian in 1+1 QED and analyzes its weak field expansion and asymptotic properties.

Findings

Three-loop Lagrangian calculated in 1+1 QED.

Weak field expansion analyzed and compared with instanton predictions.

Results support conjectures about photon amplitude growth at large N.

Abstract

In recent years, the Euler-Heisenberg Lagrangian has been shown to be a useful tool for the analysis of the asymptotic growth of the N-photon amplitudes at large N. Moreover, certain results and conjectures on its imaginary part allow one, using Borel analysis, to make predictions for those amplitudes at large loop orders. Extending work by G.V. Dunne and one of the authors to the three-loop level, but in the simpler context of 1+1 dimensional QED, we calculate the corresponding Euler-Heisenberg Lagrangian, analyse its weak field expansion, and study the congruence with predictions obtained from worldline instantons. We discuss the relevance of these issues for Cvitanovic's conjecture.