  I propose that the proper framework for gravitational scattering theory is
the rep- resentation theory of the super-BMS algebra of Awada, Gibbons and
Shaw[1], and its generalizations. Certain representation spaces of these
algebras generalize the Fock space of massless particles. The algebra is
realized in terms of operator valued measures on the momentum space dual to
null infinity, and particles correspond to smearing these measures with delta
functions. I conjecture that scattering amplitudes defined in terms of
characteristic measures on finite spherical caps, the analog of
Sterman-Weinberg jets[2], will have no infrared (IR) divergences. An important
role is played by singular functions concentrated at zero momentum, and I argue
that the formalism of Holographic Space- Time is the appropriate regulator for
the singularities. It involves a choice of a time-like trajectory in Minkowski
space. The condition that physics be independent of this choice of trajectory
is a strong constraint on the scattering matrix. Poincare invariance of S is a
particular consequence of this constraint. I briefly sketch the modifications
of the formalism, which are necessary for dealing with massive particles. I
also sketch how it should generalize to AdS space-time, and in particular show
that the fuzzy spinor cutoff of HST implements the UV/IR correspondence of
AdS/CFT.
