Pseudodifferential Calculi for Magnetic Systems and Their Semiclassical Limits
Pseudodifferential calculi, also known as Weyl calculi, have become a robust mathematical tool to derive perturbation expansions and semiclassical limit. Müller and Mantoiu and Purice independently proposed a way to include magnetic fields on the level of the pseudodifferential calculus. In this talk, I will explain how this manifestly gauge-covariant formulation can be applied to obtain semiclassical limits in several settings. The simplest concerns a single quantum particle, the next level makes the Born-Oppenheimer approximation rigorous. Lastly, we will outline a magnetic pseudodifferential calculus meant for dissipative and open quantum systems.
