We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens the possibility of defining rigorously the constraints of quantum gravity as geometrical operators acting on the space of Vassiliev invariants of spin nets. We show how to explicitly realize the diffeomorphism constraint on this space and present proposals for the construction of Hamiltonian constraints. © 1998 Published by Elsevier Science B.V.
Publication Source (Journal or Book title)
Nuclear Physics B
Gambini, R., Griego, J., & Pullin, J. (1998). Vassiliev invariants: A new framework for quantum gravity. Nuclear Physics B, 534 (3), 675-696. https://doi.org/10.1016/S0550-3213(98)80012-6