In this talk I will discuss some advances in scattering theory of the massless Nelson model, which is a toy model for Quantum Electrodynamics. They include the existence of scattering states of two electrically neutral particles (`atom-atom scattering') and of one neutral and one charged particle (`atom-electron scattering').
The existence of two-particle scattering states requires detailed information about localization of each particle in space. This is encoded in infrared regularity properties of the ground state wave functions of the model w.r.t. the total momentum. I will explain how to verify these properties using theory of non-commutative recurrence relations combined with iterative analytic perturbation theory.
The talk is based on joint works with A. Pizzo.