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Anomaly freedom has been one of the most important issues in canonicalquantization of gravity. In a physically meaningful (anomaly free) theory, theconstraint operators must be first class, and their commutator algebra isexpected to resemble the corresponding classical Poisson-bracket algebra. Inthis paper, we review the "constructive" approach to obtaining a consistent setof constraints: start with a Hamiltonian constraint and generate thecorresponding diffeomorphism constraint as a commutator of two Hamiltonians.Closure of the constraint operator algebra then requires that thediffeomorphism operator obtained in this way weakly commutes with anotherHamiltonian constraint operator. The same procedure can be used to check theconsistency of some proposed quantization schemes that present a candidateHamiltonian constraint, which we do for a spherically symmetric model.

On anomaly freedom in spherically symmetric lattice loop quantization