Non-Perturbative Particle Dynamics

TL;DR

This paper develops a non-perturbative method to derive single-valued solutions for the metric and particle dynamics in (2+1)-dimensional gravity, effectively handling multivalued coordinate issues and extending to N-body systems.

Contribution

It introduces a Coulomb gauge approach that maps multivalued coordinates to single-valued ones, solving non-abelian monodromies in (2+1)-gravity.

Findings

Constructed explicit non-perturbative solutions for two particles

Mapped multivalued coordinates to single-valued solutions

Applicable to general N-body gravitational systems

Abstract

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 particles's momenta and can be applied also to the general N-body case.