QED perturbation theory has been conjectured to break down in sufficiently strong backgrounds, obstructing the analysis of strong-field physics. We show that the breakdown occurs even in classical electrodynamics, at lower field strengths than previously considered, and that it may be cured by resummation. As a consequence, an analogous resummation is required in QED. A detailed investigation shows, for a range of observables, that unitarity removes diagrams previously believed to be responsible for the breakdown of QED perturbation theory.

• Received 5 February 2021
• Revised 11 May 2021
• Accepted 30 June 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.061601

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Published by the American Physical Society