The goal of scattering theory is to describe the asymptotic evolution of systems of interacting particles. A central concept in this area is asymptotic completeness, which asserts that every state can be decomposed into bound and scattering states. While asymptotic completeness is well understood in non-relativistic classical and quantum systems, it still remains a difficult open problem in quantum field theory..
In this talk, I will review the scattering theory of quantum mechanical systems and explain conceptual and mathematical challenges of establishing asymptotic completeness in quantum field theory. I will outline essential analytic tools, such as propagation estimates, the Mourre estimate, and the convergence of the asymptotic velocity, and their role in proving asymptotic completeness..
Moreover, I will present ongoing work on the scattering theory of the Galilean-invariant Lee model, a non-relativistic quantum field theory model that describes several species of particles that can combine or decay into other particles. I will discuss how tools such as propagation estimates and the Mourre estimate from quantum mechanics can be adapted to this model to establish asymptotic completeness..

https://indico.math.cnrs.fr/event/15771/