The space of states of quantum gravity in terms of loops and extended loops: some remarks

TL;DR

This paper reviews various loop-based approaches to quantum gravity, discusses their challenges, and proposes a new formalism for 'thickened out loops' to address covariance and regularization issues.

Contribution

It introduces a novel 'thickened out loops' formalism that potentially overcomes covariance and regularization problems in loop quantum gravity.

Findings

Identifies pitfalls in existing loop and extended loop solutions.

Proposes a formalism for 'thickened out loops' that may improve regularization.

Highlights issues of covariance in extended loop approaches.

Abstract

This article reviews the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops. We discuss pitfalls of several of the results and in particular discuss the issues of covariance and regularization of the constraints in terms of extended loops. We also propose a formalism for ``thickened out loops'' which does not face the covariance problems of extended loops and may allow to regularize expressions in a consistent manner.