1. How the Jones polynomial gives rise to physical states of quantum general relativity
- Author
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Jorge Pullin, Rodolfo Gambini, and Bernd Bruegmann
- Subjects
High Energy Physics - Theory ,Physics ,Physics and Astronomy (miscellaneous) ,General relativity ,FOS: Physical sciences ,Mathematics::Geometric Topology ,Knot theory ,Hamiltonian constraint ,High Energy Physics - Theory (hep-th) ,Quantum gravity ,Diffeomorphism ,Diffeomorphism constraint ,Quantum ,Knot (mathematics) ,Mathematical physics - Abstract
Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by considering loop functionals which are knot invariants, there remains the puzzle why several of the known knot invariants are also solutions to the hamiltonian constraint. We show how the Jones polynomial gives rise to an infinite set of solutions to all the constraints of quantum gravity thereby illuminating the structure of the space of solutions and suggesting the existance of a deep connection between quantum gravity and knot theory at a dynamical level., 7pp
- Published
- 1993
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