Vassiliev invariants: a new framework for quantum gravity

Details Vassiliev invariants: a new framework for quantum gravity Vassiliev invariants: a new framework for quantum gravity

1998-03-05

arxiv.org/abs/gr-qc/9803018v1

Nucl.Phys. B534 (1998) 675-696

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, several figures included with psfig

Scientific paper

10.1016/S0550-3213(98)80012-6

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.

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