Time in (2+1)-Dimensional Quantum Gravity

TL;DR

This paper examines three different approaches to the problem of time in 2+1 dimensional quantum gravity, comparing their conceptual frameworks and implications.

Contribution

It provides a comparative analysis of the internal Schrödinger approach, Wheeler-DeWitt equation, and covariant canonical quantization in the context of 2+1 dimensional quantum gravity.

Findings

Different approaches offer unique insights into the problem of time.

The internal Schrödinger approach uses mean extrinsic curvature as a time variable.

Covariant canonical quantization introduces evolving constants of motion.

Abstract

General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt equation, and covariant canonical quantization with ``evolving constants of motion.'' (To appear in {\em Proc.\ of the Lanczos Centenary Conference}, Raleigh, NC, December 1993.)