Non-perturbative particle dynamics in (2+1)-gravity

We construct a non-perturbative, single-valued solution for the metric and the motion of two interacting particles in (2 + 1)-gravity, by using a Coulomb gauge of conformal type. The method provides the mapping from multivalued (Minkowskian) coordinates to single-valued ones, which solves the non-abelian monodromies due to particlesʹ momenta and can be applied also to the general N-body case.