The Constraints of 2+1 Quantum Gravity

TL;DR

This paper discusses the constraints in 2+1 dimensional quantum gravity, comparing different formalisms and introducing an operator algebra approach, with insights into quantization methods and their relation to four-dimensional theories.

Contribution

It provides a comparative analysis of second and first order formalisms in 2+1 gravity and introduces an operator algebra approach for quantization.

Findings

Comparison of formalisms in 2+1 gravity

Development of an operator algebra quantization method

Discussion of the g=1 case in quantum gravity

Abstract

To appear in proceedings of II Workshop on ``Constraints Theory and Quantisation Methods''Montepulciano (Siena) 1993} General discussion of the constraints of 2+1 gravity, with emphasis on two approaches, namely the second order and first order formalisms, and comparison with the four dimensional theory wherever possible. Introduction to an operator algebra approach that has been developed in the last few years in collaboration with T.Regge, and discussion of the quantisation of the g=1 case.