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

Preprint

21 September 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.gr-qc/9909063

Abstract

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.

Keywords

ALGEBRA OF CONSTRAINTS
CANONICAL QUANTIZATION
CONSISTENT CANONICAL
GENERAL RELATIVITY
VASSILIEV KNOT
QUANTIZATION
COMMUTATORS
GRAVITY

All Related Versions

Version 1, 1999-09-21, ArXiv
Published version: Physical Review Letters, 84 (11), 2314.

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