Infrared finite scattering theory in quantum field theory and quantum gravity

It has been known since the earliest days of quantum field theory (QFT) that infrared divergences arise in scattering with massless fields. These are manifestations memory effect: At order $1/r$ a generically will not return to same value at late retarded times ($u\ensuremath{\rightarrow}+\ensuremath{\infty}$) as it had early ($u\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$). There is nothing singular about states memory, but they do lie standard Fock space. Infrared merely artifacts trying represent If one interested only quantities directly relevant collider physics, can be successfully dealt by imposing an cutoff, calculating inclusive quantities, and then removing cutoff. However, this approach does allow treat observable highly unsatisfactory if wishes view $S$-matrix fundamental quantity QFT gravity, itself undefined. In have well-defined $S$-matrix, necessary define ``in'' ``out'' Hilbert spaces incorporate satisfactory way. Such construction was given Faddeev Kulish for electrodynamics (QED) massive charged field. Their understood pairing momentum eigenstates particles corresponding representations electromagnetic produce vanishing large gauge charges spatial infinity. (This procedure usually referred ``dressing'' particles.) We investigate QED show that, consequence collinear divergences, required dressing case infinite total energy flux, so obtained Faddeev-Kulish unphysical. An additional difficulty arises Yang-Mills theory, due fact ``soft particles'' used contribute charge-current thereby invalidating construct there insufficiently many charge accommodate theory. analog would attempt space supertranslation Again, desired because contributes null flux. prove no infinity apart from vacuum. Thus, analogs fail catastrophically gravity. some alternatives constructions find these also work. believe level gravity---as well theory---it algebraic viewpoint on states, wherein ``shoehorn'' into prechosen spaces. outline framework such which manifestly finite.