Diffeomorphism symmetry in quantum gravity models

TL;DR

This paper reviews the role of diffeomorphism symmetry in quantum gravity models, emphasizing the importance of understanding both exact and approximate symmetries for accurate continuum limits.

Contribution

It provides a framework for identifying and incorporating exact and approximate diffeomorphism symmetries in quantum gravity models.

Findings

Exact symmetries can be preserved in discretized models.

Approximate symmetries emerge due to discretization.

Proper treatment of symmetries is crucial for continuum limit accuracy.

Abstract

We review and discuss the role of diffeomorphism symmetry in quantum gravity models. Such models often involve a discretization of the space-time manifold as a regularization method. Generically this leads to a breaking of the symmetries to approximate ones, however there are incidences in which the symmetries are exactly preserved. Both kind of symmetries have to be taken into account in covariant and canonical theories in order to ensure the correct continuum limit. We will sketch how to identify exact and approximate symmetries in the action and how to define a corresponding canonical theory in which such symmetries are reflected as exact and approximate constraints.