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 three-space. 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 closed-form 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 three-manifold.
- 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)