How the Jones polynomial gives rise to physical states of quantum general relativity
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.
 Publication:

General Relativity and Gravitation
 Pub Date:
 January 1993
 DOI:
 10.1007/BF00756923
 arXiv:
 arXiv:hepth/9203040
 Bibcode:
 1993GReGr..25....1B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 7pp