Comment on "Towards a quantum notion of covariance in spherically symmetric loop quantum gravity"

TL;DR

This paper critically examines a recent claim of achieving covariance in spherically symmetric loop quantum gravity models, revealing that the proposed approach violates the fundamental hypersurface deformation structure, thus challenging its validity.

Contribution

The paper provides a detailed critique showing that the new constructions claiming covariance actually violate key gauge transformation properties in spherically symmetric models.

Findings

The proposed covariance construction violates hypersurface deformation constraints.

Previous obstacles to covariance in these models remain unresolved.

The critique questions the validity of the recent progress claimed in the literature.

Abstract

A recent paper promises new constructions that may make it possible to achieve covariance in spherically symmetric models of loop quantum gravity. This claim is contrary to the discovery of several stubborn obstacles to covariance uncovered in the same models during the last few years. As the authors point out in their abstract, new progress is supposedly possible if one takes into account crucial features of a certain partial Abelianization of the gauge transformations of spherically symmetric gravity, published by the same authors. In canonical form, these gauge transformations are given by hypersurface deformations. A closer inspection of the technical calculations shows that spherically symmetric hypersurface deformations are, in fact, violated in the construction.