Decoding the Path Integral: Resurgence and Extreme Physics

How do quantum systems behave under extreme conditions such as ultra-high density and ultra-high intensity? This question has applications in a wide range of physical contexts, from condensed matter to particle and nuclear physics, and to astrophysics. The answer requires going beyond perturbation theory, directly to the path integral representation of quantum field theory. However, there are several important conceptual and computational problems concerning quantum path integrals under extreme conditions, which have recently been approached from new perspectives motivated by "resurgent asymptotics", a novel mathematical formalism that effectively unifies perturbative and non-perturbative physics. This talk will review the basic ideas behind the connections between resurgent asymptotics and physics, starting from the work of Airy and Stokes on rainbows, and the development of trans-series by Ecalle, and then turn to some recent applications in quantum mechanics and quantum field theory.