Point particles in 2+1 dimensions: toward a semiclassical loop gravity formulation

TL;DR

This paper develops a semiclassical loop gravity framework for point particles in 2+1 dimensions by using a dynamical triangulation approach to analyze the gravitational system and its boundary properties.

Contribution

It introduces a novel triangulation-based method to connect point particle dynamics with loop gravity phase space in 2+1 dimensions.

Findings

Hamiltonian reduces to a boundary term representing total mass

Triangulation transitions occur when particles meet edges

Framework links point particle dynamics with loop gravity phase space

Abstract

We study point particles in 2+1 dimensional first order gravity using a triangulation to fix the connection and frame-field. The Hamiltonian is reduced to a boundary term which yields the total mass. The triangulation is dynamical with non-trivial transitions occurring when a particle meets an edge. This framework facilitates a description in terms of the loop gravity phase space.