# Note on the conjectured breakdown of QED perturbation theory in strong fields

## TL;DR

This paper investigates the behavior of QED in strong fields, showing that the expected breakdown of perturbation theory at high quantum nonlinearity does not occur at high energy, challenging previous conjectures based on constant background assumptions.

## Contribution

The study demonstrates that in realistic plane wave backgrounds, loop corrections decrease with increasing quantum nonlinearity at high energy, contrasting prior predictions of divergence.

## Key findings

- Loop contributions decrease with quantum nonlinearity at high energy.
- Observables scale differently in finite-duration plane waves compared to constant backgrounds.
- Challenges the conjecture of perturbation theory breakdown in strong fields.

## Abstract

Strong background fields require a non-perturbative treatment, which is afforded in QED by the Furry expansion of scattering amplitudes. It has been conjectured that this expansion breaks down for sufficiently strong fields, based on the asymptotic growth of loop corrections with increasing "quantum nonlinearity", essentially the product of field strength and particle energy. However, calculations to date have assumed that the background is constant. We show here, using general plane waves of finite duration, that observables at high quantum nonlinearity scale differently depending on whether intensity or energy is large. We find that, at high energy, loop contributions to observables tend to fall with increasing quantum nonlinearity, rather than grow.