Vassiliev invariants: a new framework for quantum gravity

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.

15 pages, several figures included with psfig

References in corpus (1)

• Chern--Simons states in spin-network quantum gravity

Cited by in corpus (6)

• Loop quantum gravity and quanta of space: a primer
• Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants
• Diffeomorphism invariant Quantum Field Theories of Connections in terms of webs
• Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra
• Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure
• Embedded graph invariants in Chern-Simons theory