On the diffeomorphism commutators of lattice quantum gravity

TL;DR

This paper demonstrates that the algebra of discretized spatial diffeomorphism constraints in lattice quantum gravity closes without anomalies as the lattice spacing approaches zero, regardless of factor-ordering or discretization method.

Contribution

It generalizes previous results by showing anomaly-free closure of the algebra for various discretizations and factor-orderings in lattice quantum gravity.

Findings

Algebra closes without anomalies in the continuum limit

Results hold for arbitrary factor-ordering

Applicable to multiple discretization schemes

Abstract

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a variety of different discretizations of the continuum constraints, and thus generalizes an earlier calculation by Renteln.