Non-perturbative 2 particle scattering amplitudes in 2+1 dimensional quantum gravity

Abstract

A quantum theory for scalar particles interacting only gravitationally in 2+1 dimensions is considered. Since there are no real gravitons the interaction is entirely topological. Nevertheless, there is non-trivial scattering. We show that the two-particle amplitude can be computed exactly. Although the complete "theory" is not well understood we suggest an approach towards formulating theN particle problem.