The Status of Diffeomorphism Superselection in Euclidean 2+1 Gravity

TL;DR

This paper investigates superselection laws in loop quantum gravity, demonstrating that in 2+1 Euclidean gravity these laws are spurious, which clarifies their role in the quantization process.

Contribution

It shows that certain superselection laws in loop quantum gravity are spurious in 2+1 Euclidean gravity, aiding the understanding of the diffeomorphism constraint.

Findings

Superselection laws are spurious in 2+1 Euclidean gravity.

Loop representation and Refined Algebraic Quantization can still produce the usual quantum theory.

Clarifies the technical nature of superselection laws in quantum gravity.

Abstract

This work addresses a specific technical question of relevance to canonical quantization of gravity using the so-called new variables and loop-based techniques of Ashtekar, Rovelli, and Smolin. In particular, certain `superselection laws' that arise in current applications of these techniques to solving the diffeomorphism constraint are considered. Their status is elucidated by studying an analogous system: 2+1 Euclidean gravity. For that system, these superselection laws are shown to be spurious. This, however, is only a technical difficulty. The usual quantum theory may still be obtained from a loop representation and the technique known as `Refined Algebraic Quantization.'