  We consider the interaction between a matter system and soft gravitons. We
use a functional eikonal expansion to deal with the infrared divergences, and
introduce a "composite generating functional" which allows us to calculate a
decoherence functional for the time evolution of the system. These techniques
allow us to formulate scattering problems in a way which deals consistently
with infrared effects, as well as being manifestly diffeomorphism invariant. We
show how the asymptotic form of the decoherence functional can be written in
terms of the infinitely many conserved charges associated with asymptotic BMS
symmetries, and allow us to address the question of how much information is
lost during the scattering.
