Polygon model from first order gravity

TL;DR

This paper reconstructs a polygon model for 2+1 gravity with point particles from the first order formalism, confirming the symplectic structure aligns with the canonical formulation.

Contribution

It introduces a new derivation of the polygon model directly from the first order variables, clarifying its symplectic structure.

Findings

The symplectic structure matches the canonical one.

The polygon model is explicitly reconstructed from triad and spin connection variables.

The approach applies to arbitrary numbers of spinless point particles.

Abstract

The gauge fixed polygon model of 2+1 gravity with zero cosmological constant and arbitrary number of spinless point particles is reconstructed from the first order formalism of the theory in terms of the triad and the spin connection. The induced symplectic structure is calculated and shown to agree with the canonical one in terms of the variables.