On quantum propagation in Smolin's weak coupling limit of 4d Euclidean Gravity

Understand

Two desireable properties of a quantum dynamics for Loop Quantum Gravity (LQG) are that its generators provide an anomaly free representation of the classical constraint algebra and that physical states which lie in the kernel of these generators encode propagation.

• A physical state in LQG is expected to be a sum over graphical $SU(2)$ spin network states.
• By propagation we mean that a quantum perturbation at one vertex of a spin network state propagates to vertices which are `many links away' thus yielding a new spin network state which is related to the old one by this propagation.
• A physical state encodes propagation if its spin network summands are related by propagation.