Canonical quantum gravity in the Vassiliev invariants arena:II. Constraints, habitats and consistency of the constraint algebra

Abstract

In a companion paper we introduced a kinematical arena for the discussionof the constraints of canonical quantum gravity in the spin networkrepresentation based on Vassiliev invariants. In this paper weintroduce the Hamiltonian constraint, extend the space of states tonon-diffeomorphism-invariant `habitats' and check that the off-shellquantum constraint commutator algebra reproduces the classical Poissonalgebra of constraints of general relativity without anomalies. Onecan therefore consider the resulting set of constraints and space ofstates as a consistent theory of canonical quantum gravity.