Knot theory and quantum gravity
Abstract
A new representation for quantum general relativity is described, which is defined in terms of functionals of sets of loops in threespace. In this representation, exact solutions of the quantum constraints may be obtained. This result is related to the simplification of the constraints in the new formalism of Ashtekar (1986). A closedform general solution is given for the diffeomorphism constraints, and a large class of solutions is given for the full set of constraints. These are classified by the knot and link classes of the spatial threemanifold.
 Publication:

Physical Review Letters
 Pub Date:
 September 1988
 DOI:
 10.1103/PhysRevLett.61.1155
 Bibcode:
 1988PhRvL..61.1155R
 Keywords:

 Canonical Forms;
 Gravitation;
 Manifolds (Mathematics);
 Quantum Theory;
 04.60.+n;
 02.40.+m;
 Physics (General)