Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants

Details Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants

1999-09-21

arxiv.org/abs/gr-qc/9909063v1

Phys.Rev.Lett. 84 (2000) 2314-2317

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, RevTex, one figure

Scientific paper

10.1103/PhysRevLett.84.2314

We present a quantization of the Hamiltonian and diffeomorphism constraint of canonical quantum gravity in the spin network representation. The novelty consists in considering a space of wavefunctions based on the Vassiliev knot invariants. The constraints are finite, well defined, and reproduce at the level of quantum commutators the Poisson algebra of constraints of the classical theory. A similar construction can be carried out in 2+1 dimensions leading to the correct quantum theory.

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