Resurgence and Extreme Field QFT

I propose a new approach to multi-loop QFT computations in strong background fields, based on an application of resurgent asymptotics to the extraction of strong-field and non-perturbative information from a limited number of terms of a weak-field expansion. The proposed method is demonstrated explicitly with the one-loop and two-loop expressions for the QED Euler-Heisenberg effective action, for which a surprising amount of strong-field and non-perturbative physics may be derived from just 10 terms of a weak magnetic field expansion. I will also discuss applications to inhomogeneous fields.