Schwinger-Keldysh effective field theory

Abstract

The subject of quantum field theory in mixed states of quantum matter is an old and rich one. The natural setting to discuss field theory in a mixed state is the Schwinger-Keldysh formalism. The subject of this talk is the set of peculiar symmetries that arise in Schwinger-Keldysh theories, and how they may be accounted for in effective field theory. In particular, when the mixed state is thermal, the effective description is constrained by two BRST-like supercharges which, at low energies, generate an algebra akin to minimal supersymmetric quantum mechanics. If time allows, I will also discuss a sort of Schwinger-Keldysh bootstrap for effective actions on more complicated closed-time-contours, which describe the out-of-time-ordered correlation functions that diagnose early-time chaotic growth in quantum systems.