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

TL;DR

This paper develops a consistent quantum gravity framework using Vassiliev invariants, introducing Hamiltonian constraints and habitats, and verifying the anomaly-free constraint algebra.

Contribution

It extends the spin network representation with Vassiliev invariants by defining Hamiltonian constraints and habitats, ensuring a consistent off-shell quantum constraint algebra.

Findings

The quantum constraint algebra reproduces the classical Poisson algebra without anomalies.

The extended space of states includes non-diffeomorphism invariant habitats.

The framework provides a consistent set of constraints for canonical quantum gravity.

Abstract

In a companion paper we introduced a kinematical arena for the discussion of the constraints of canonical quantum gravity in the spin network representation based on Vassiliev invariants. In this paper we introduce the Hamiltonian constraint, extend the space of states to non-diffeomorphism invariant ``habitats'' and check that the off-shell quantum constraint commutator algebra reproduces the classical Poisson algebra of constraints of general relativity without anomalies. One can therefore consider the resulting set of constraints and space of states as a consistent theory of canonical quantum gravity.