Quantum Gravity and Equivariant Cohomology
R. Brooks, G. Lifschytz
TL;DR
This paper presents a method to derive quantum gravity correlation functions and wavefunctionals using topological invariants, with detailed examples in three and four dimensions, advancing the understanding of quantum gravity's mathematical structure.
Contribution
It introduces a novel procedure linking Donaldson invariants from topological quantum field theories to quantum gravity wavefunctionals, applicable in three and four dimensions.
Findings
Explicit expressions for 3D wavefunctionals derived from topological invariants
A normalization procedure for quantum gravity wavefunctionals proposed
Application of the method to both 3D and 4D quantum gravity cases
Abstract
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 \sbft{}, are given in the three dimensional case. A procedure for normalizing these wavefunctionals is proposed.
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