Asymptotic Electromagnetic Fields in Models of Quantum-Mechanical Matter Interacting with the Quantized Radiation Field

In models of (non-relativistic and pseudo-relativistic) electrons interacting with static nuclei and with the (ultraviolet-cutoff) quantized radiation field, the existence of asymptotic electromagnetic fields is established. Our results yield some mathematically rigorous understanding of Rayleigh scattering and of the phenomenon of relaxation of isolated atoms to their ground states. Our proofs are based on propagation estimates for electrons inspired by similar estimates known from $N$-body scattering theory.