Polygon model from first order gravity

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.

20 pages, presentation improved, typos corrected

References in corpus (14)

• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
• Symplectic structure of the moduli space of flat connections on a Riemann surface
• On the relation between 2+1 Einstein gravity and Chern Simons theory
• Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions
• Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity
• The Phase Space Structure of Multi Particle Models in 2+1 Gravity
• Three Dimensional Canonical Quantum Gravity
• New Loop Representations for 2+1 Gravity
• Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles
• Geometric Cone Surfaces and (2+1)- Gravity coupled to Particles
• $2+1$ Covariant Lattice Theory and t'Hooft's Formulation
• Quantisation of 2+1 gravity for genus 2
• (2+1) gravity for higher genus in the polygon model

Cited by in corpus (7)

• Quantum geometry from phase space reduction
• The Hamiltonian constraint in 3d Riemannian loop quantum gravity
• Timelike surfaces in Lorentz covariant loop gravity and spin foam models
• A locally finite model for gravity
• Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity
• Collisions in piecewise flat gravity in 3+1 dimensions
• Point particles in 2+1 dimensions: general relativity and loop gravity descriptions