Scattering theory of infrared divergent Pauli-Fierz Hamiltonians

We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz Hamiltonians. We show that the CCR representations obtained from the asymptotic field contain so-called coherent sectors describing an infinite number of asymptotically free bosons. We formulate some conjectures leading to mathematically well defined notion of inclusive and non-inclusive scattering cross-sections for Pauli-Fierz Hamiltonians. Finally we give a general description of the scattering theory of QFT models in the presence of coherent sectors for the asymptotic CCR representations.