QUANTUM ASPECTS OF 2+1 GRAVITY

TL;DR

This paper reviews recent efforts to quantize 2+1 dimensional gravity, focusing on connection and ADM formulations, and discusses their progress and potential equivalences in the quantum regime.

Contribution

It systematically compares different quantization approaches for 2+1 gravity, highlighting their methodologies and evaluating their quantum equivalences.

Findings

Progress in canonical quantization of 2+1 gravity using Wilson loops

Comparison of connection and ADM formulations in quantum context

Discussion on potential quantum equivalences of different approaches

Abstract

We review and systematize recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space-times $\R\times\Sigma^g$, where $\Sigma^g$ is a compact Riemann surface of genus $g$. The emphasis is on quantizations of the classical connection formulation, which use Wilson loops as their basic observables, but also results from the ADM formulation are summarized. We evaluate the progress and discuss the possible quantum (in)equivalence of the various approaches.