  Although an important issue in canonical quantization, the problem of
representing the constraint algebra in the loop representation of quantum
gravity has received little attention. The only explicit computation was
performed by Gambini, Garat and Pullin for a formal point-splitting
regularization of the diffeomorphism and Hamiltonian constraints. It is shown
that the calculation of the algebra simplifies considerably when the
constraints are expressed not in terms of generic area derivatives but rather
as the specific shift operators that reflect the geometric meaning of the
constraints.

General Relativity and Quantum Cosmology