How the Jones polynomial gives rise to physical states of quantum general relativity
Mar, 19927 pages
Published in:
- Gen.Rel.Grav. 25 (1993) 1-6
e-Print:
- hep-th/9203040 [hep-th]
DOI:
Report number:
- SU-GP-92-3-1
Citations per year
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.- quantum gravity: representation
- loop space
- knot theory: Jones polynomial
- Chern-Simons term
- Wheeler-DeWitt equation: solution
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