The Fox and the Hedgehog Series - “The breakdown of perturbation theory: physics in strong fields”

Perturbation theory (expanding interesting quantities in a power series of some small parameter) is a physicist’s go-to tool for solving pretty much anything. It’s enormously useful. Mathematically, there is a huge body of literature on the summation, convergence, and resummation of possibly divergent series. In this talk I’ll give a very low-level introduction to the overlap of these ideas in the context of my research, which is quantum field theory in the presence of extremely strong electromagnetic and gravitational fields, so strong that perturbative methods go out the window. The talk will be technically very simple (I’ll only use toy models) and I’ll only try to convey a sense of the big problems and why they’re interesting (at least to me).