Loop quantum gravity: an outside view

TL;DR

This paper critically reviews loop quantum gravity, emphasizing the importance of constraint algebra closure for quantum spacetime covariance, and discusses the challenges posed by ambiguities and the development of approximation methods.

Contribution

It provides a pedagogical yet critical assessment of loop quantum gravity, highlighting the significance of off-shell closure and the difficulties in connecting with classical and particle physics.

Findings

Emphasizes the importance of constraint algebra closure for theory consistency

Identifies numerous ambiguities in Hamiltonian constraint formulation

Highlights the challenge of developing approximation methods for classical and particle physics connection

Abstract

We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a crucial test of quantum space-time covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge.