Some General Problems in Quantum Gravity II: The Three Dimensional Case

TL;DR

This paper reviews the mathematical challenges in defining the path integral measure in three-dimensional quantum gravity, extending previous work on four dimensions and proposing directions for future research.

Contribution

It extends prior analysis of quantum gravity to the three-dimensional case, focusing on the measure problem and suggesting potential avenues for progress.

Findings

Identifies key mathematical issues in 3D quantum gravity

Connects 3D and 4D quantum gravity problems

Proposes future research directions

Abstract

The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed as an extension of a preceding one on the four dimensional case (\cite{kn:eav5}), where also some general ideas are discussed in detail. We finally put forward some suggestions on the lines one could expect further progress in the field.