ar X iv : h ep - t h / 93 08 12 6 v 1 2 6 A ug 1 99 3 TOPOLOGICAL FIELD THEORY AS THE KEY TO QUAN - TUM GRAVITY

by: Louis Crane, mathematics department,KSU presented to the conference on knot theory and quantum gravity Riverside California Abstract: Motivated by the similarity between CSW theory and the Chern Simons state for General Relativity in the Ashtekar variables, we explore what a universe would look like if it were in a state corresponding to a 3D TQFT. We end up with a construction of propagating states for parts of the universe and a Hilbert space corresponding to a certain approximation. The construction avoids path integrals, using instead recombination diagrams in a very special tensor category. 1. INTRODUCTION What I wish to propose is that the quantum theory of gravity can be constructed from a topological field theory. Notice, I do not say that it is a topo-logical field theory. Physicists will be quick to point out that there are local excitations in gravity, so it cannot be topological. Nevertheless, the connections between general relativity in the loop formulation and the CSW TQFT are very suggestive. Formally, at least, the CSW action term