A procedure for obtaining correlation function densities and wavefunctionals for quantum gravity from the Donaldson polynomial invariants of topological quantum field theories, is given. We illustrate how our procedure may be applied to three and four dimensional quantum gravity. Detailed expressions, derived from super-BF gauge theory, are given in the three dimensional case. A procedure for normalizing these wavefunctionals is proposed.
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Topological invariants on a manifold are a subset of diffeomorphism invariants. Thus we expect that elements of the set of topological invariants should be a subset of the quantum gravity observables. Additionally, it is generally believed that observables, which are elements of the BRST complex, may be used to construct vertex operators or wavefunctionals for the theory. Consequently, should we succeed in constructing observables for quantum gravity, we might also be able to construct wavefunctionals. These statements form the nexus for the present work. The puzzle is how to find representations of topological invariants in quantum gravity theories in sufficient generality so as not to explicitly exploit the topological nature of low-dimensional gravitational theories. In this paper, we will give a formal procedure for constructing operators which have the * This work is supported in part by funds provided by the US Department of Energy (DOE) under cooperative agreement DE-FC02-94ER40818. l E-mail: email@example.com 2 E-mail: gill @irene.mit.edu
ASJC Scopus subject areas
- Nuclear and High Energy Physics