Multiloop Euler-Heisenberg Lagrangians, Schwinger pair creation, and the QED N - photon amplitudes

TL;DR

This paper discusses a three-loop check of a conjecture related to the Euler-Heisenberg Lagrangian in QED, using a simplified 1+1 dimensional model to develop new computational methods and representations.

Contribution

It introduces trigonometric integral representations and a symmetry-based method for calculating weak-field expansion coefficients at three loops in QED.

Findings

Developed trigonometric integral representations for three-loop contributions.

Created a symmetry-based method for weak-field expansion calculations.

Provided insights into the imaginary part of the Euler-Heisenberg Lagrangian.

Abstract

An update is given on our long-term effort to perform a three-loop check on the Affleck-Alvarez-Manton/Lebedev-Ritus exponentiation conjecture for the imaginary part of the Euler-Heisenberg Lagrangian, using 1+1 dimensional QED as a toy model. After reviewing the history and significance of the conjecture, we present trigonometric integral representations for the single electron loop contributions to the three-loop Lagrangian, and develop a symmetry-based method for the calculation of their weak-field expansion coefficients.