Vassiliev invariants: a new framework for quantum gravity
General Relativity and Quantum Cosmology
2009-10-31 v1
Abstract
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.
Cite
@article{arxiv.gr-qc/9803018,
title = {Vassiliev invariants: a new framework for quantum gravity},
author = {Rodolfo Gambini and Jorge Griego and Jorge Pullin},
journal= {arXiv preprint arXiv:gr-qc/9803018},
year = {2009}
}
Comments
15 pages, several figures included with psfig