Self-consistent scattering matrix in 2 + 1 gravity

Abstract

We set up an S-matrix approach to the quantum two-body problem in 2 + 1 gravity based on the correspondence principle and on analyticity and crossing symmetry in properly defined Mandelstam variables. The ensuing bootstrap solution is dependent on a few low partial wave parameters that we fix in the massless case so as to satisfy the unitarity bounds. The final amplitude is consistent with the recently found value of the classical scattering angle and is not purely elastic, showing matter production consistent with low order perturbation theory.