Towards a Consistent Quantum Dynamics for Euclidean LQG: A Weak Coupling Limit

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Spacetime covariance in canonical quantum gravity is tied to the existence of an anomaly free representation of its constraint algebra.  I will argue that establishing the existence of such a  representation  in the LQG context requires the consideration of   higher than unit density  weight Hamiltonian constraints. Smolin's weak coupling limit of Euclidean gravity, while simpler than full blown gravity , still exhibits an open constraint algebra isomorphic to that of gravity and offers an ideal testing ground for the investigation of the quantum constraint algebra of such higher density constraints. I will report on recent progress on this issue in the context of an LQG type quantization of this system. Certain features of the constructions such as the encoding of the action of the  quantum constraint in terms of operator valued diffeomorphisms may play a key role in the definition of a consistent quantum dynamics for LQG.