Quantum Gravity in Abelian Hypersurface Deformations

Abelianized structures in spherically symmetric hypersurface deformations: Inconsistency of a quantum notion of covariance in models of loop quantum gravity

In canonical gravity, general covariance is implemented by hypersersurface-deformation symmetries on phase space.For spherically symmetric space-times, it is possible to identify a certain abelian substructure within general hypersurface deformations, which suggests a simplified realization as a lie algebra.The generators of this substructure can be quantized more easily than full hypersurface deformations, but the symmetries they generate do not directly correspond to hypersurface-deformation symmetries.The availability of consistent quantizations therefore does not guarantee general covariance or a meaningful quantum notion thereof.