# Infrared finite scattering in QFT & quantum gravity

The "infrared problem" is the generic emission of an infinite number of low-frequency quanta in any scattering process with massless fields. The "out" state contains an infinite number of such quanta which implies that it does not lie in the standard Fock representation. Consequently, the standard S-matrix is undefined as a map between "in" and "out" states in the standard Fock space. This fact is due to the existence of a low-frequency tail of the radiation field i.e. the memory effect. In massive QED, the Faddeev-Kulish representations have been argued to yield an I.R. finite S-matrix. We clarify the "preferred " status of such representations as eigenstates of the conserved "large gauge charge'' at spatial infinity. We prove a "No-Go" theorem for the existence of a suitable Hilbert space analogously constructed in massless QED, QCD, linearized quantum gravity with massive/massless sources, and in full quantum gravity. We then suggest an "infrared-finite" formulation of scattering theory in terms of correlation functions without any a priori choice of "in/out" Hilbert spaces.