The Euler-Heisenberg Lagrangian beyond one loop

TL;DR

This paper reviews higher loop corrections to the Euler-Heisenberg Lagrangian, discusses their implications for QED perturbation series, and presents a three-loop integral representation in 1+1 dimensions using the worldline formalism.

Contribution

It provides a comprehensive review of multi-loop corrections and introduces a new three-loop integral representation in lower-dimensional QED.

Findings

Higher loop corrections are crucial for understanding QED perturbation series.

A new three-loop integral representation in 1+1 dimensions is derived.

The work advances the study of convergence properties of photon amplitudes.

Abstract

We review what is presently known about higher loop corrections to the Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those corrections as a tool for the study of the properties of the QED perturbation series is outlined. As a further step in a long-term effort to prove or disprove the convergence of the N photon amplitudes in the quenched approximation, we present a parameter integral representation of the three-loop Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline formalism.