Event

A long standing problem in QFT and quantum gravity is the construction of an “IR”-finite S-matrix. In the gravitational case, the existence of these “infrared divergences” is intimately tied to the “memory effect” (i.e. the permanent displacement of test masses due to passage of a gravitational wave) and the existence of an infinite number of conserved charges at spatial infinity. In this talk,  I shall illustrate that the construction of an IR-finite S-matrix requires the inclusion of states with memory (which do not lie in the standard Fock space).  In massive QED an elegant solution to this problem was provided by Faddeev and Kulish who constructed an incoming/outgoing Hilbert space of charged particle states “dressed” with memory. However, we show that this construction fails in the case of massless QED, linearized quantum gravity with massless/massive sources and in full, vacuum quantum gravity. We also show that “non-Faddeev-Kulish” representations are also unsatisfactory. In particular, in quantum gravity, it therefore seems that there does not appear to be any (separable) Hilbert space of incoming/outgoing states that can accommodate all scattering states. Nevertheless, the correlation functions of all scattering states are well-defined and we argue that an IR-finite scattering theory can be defined in all cases by mapping “in” correlation functions to “out” correlation functions without trying to artificially restrict states to a particular Hilbert space.