Vassiliev invariants: A new framework for quantum gravity |
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| Institution: | 1. lnstituto de Fisica, Facultad de Ciencias, Tristan Narvaja 1674, Montevideo, Uruguay;2. Center for Gravitational Physics and Geometry, Department of Physics, The Pennsylvania State University, 104 Davey Lab, University Park, PA 16802, USA;1. Instituto de Física, Facultad de Ciencias, Iguá 4225, esq. Mataojo, 11400 Montevideo, Uruguay;2. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, United States |
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| 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. |
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