Entanglement in Quantum Field Theories

Functional Analysis Seminar, Pennsylvania State University

In the first part, I will define entanglement entropy in quantum systems and review various subtleties that arise when one applies this concept to quantum field theories. In this context, I will discuss how unitarily inequivalent Fock space representations arise from different complex structures on classical phase space.
In the second part, I will explain recent results on entanglement production at instabilities. In particular, I will show that the entanglement entropy grows linearly in systems that are classically unstable in the sense of positive Lyapunov exponents. The proof will be based on the interplay between symplectic and metric geometry.