Lectures in (2+1)-Dimensional Gravity

TL;DR

This paper reviews classical and quantum aspects of gravity in three dimensions, focusing on the quantum mechanics of closed universes and (2+1)-dimensional black holes, discussing multiple formulations and approaches to quantization.

Contribution

It provides a comprehensive overview of classical formulations and quantization methods for (2+1)-dimensional gravity, summarizing various approaches and references.

Findings

Analysis of three classical formulations

Discussion of three quantization approaches

Summary of various other methods

Abstract

These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the (2+1)-dimensional black hole. Three formulations of the classical theory and three approaches to quantization are discussed in some detail, and a number of other approaches are summarized. An extensive, although by no means complete, list of references is included. (Lectures given at the First Seoul Workshop on Gravity and Cosmology, February 24-25, 1995.)