A universal concept of asymptotic completeness in non-relativistic QED

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Asymptotic completeness, which is one of the central concepts in scattering theory, requires that all the physical states of a given system have an interpretation in terms of particles. While this property is well understood in quantum mechanics, its status in quantum field theory, both relativistic and non-relativistic, is much less clear. In quantum electrodynamics even a generally accepted formulation of this concept is missing to date due to a complicated infrared structure of the theory.This project is a part of a larger enterprise aiming at a formulation of a universal concept of asymptotic completeness in quantum electrodynamics. This concept should be meaningful in each of the standard approaches to the subject, as forexample the non-relativistic, algebraic and perturbative approach. The present research objective is to find a notion of asymptotic completeness applicable to models of non-relativistic quantum electrodynamics, irrespectively of their infrared structure. This notion should be consistent with the qualitative understanding of particle aspects developed in the framework of algebraic quantum field theory.