The Phase Space of 2+1 Dimensional Gravity in the Ashtekar Formulation

TL;DR

This paper explores the phase space of 2+1 dimensional gravity using the Ashtekar formulation, revealing new constraint systems and demonstrating a larger degrees of freedom than traditional approaches.

Contribution

It introduces two new first class constraint systems in the Ashtekar formulation and analyzes the implications of degenerate solutions for the theory's degrees of freedom.

Findings

Discovery of two new first class constraint systems.

Identification of degenerate sectors in the Ashtekar formulation.

Demonstration of arbitrarily large degrees of freedom.

Abstract

The Ashtekar formulation of 2+1 gravity differs from the geometrodynamical and Witten descriptions when the 2-metric is degenerate. We study the phase space of 2+1 gravity in the Ashtekar formulation to understand these degenerate solutions to the field equations. In the process we find two new systems of first class constraints which describe part of the degenerate sectors of the Ashtekar formulation. One of them also generalizes the Witten constraints. Finally we argue that the Ashtekar formulation has an arbitrarily large number of degrees of freedom in contrast to the usual descriptions. TO GET THE FIGURES CONTACT Barbero@suhep.phy.syr.edu or Madhavan@suhep.phy.syr.edu