The No-Boundary Wave Function
Simplicial Approximation
The papers on this page are mostly concerned with extending the simplicial approximation to the NBWF of the previous page in various directions, in particular sums over topologies. 
Simplical Quantum Gravity and Unruly Topology [71]
This paper reviews the simplical approximation to the NBWF on the previous page but also discusses the sum over topologies.
Unruly Topology in Two-Dimensional Quantum Gravity [65]
A geometry is a manifold with a metric. In a sum-over-histories formulation of quantum gravity it would seem natural to sum over manifolds as well as metrics. (A sum over topologies.) But as described also in [62] it is not straightforward to sum over manifolds in four-dimensions because the problem of deciding when two manifolds are topologically equivalent is unsolvable. The requirement that a geometry be a manifold is a mathematical implementation of the principle of equivalence. In a very simple two dimensional model this paper investigates whether the quantum sum should be over a larger but classifiable category of simplicial complexes with manifolds dominating in the classical limit.
The Signature of Simplicial Superspace [111]
(with W. Miller and Ruth Williams) This is concerned with the (DeWitt) metric on the superspace of simplical three-geometries that can be used to construct a generalized quantum mechanics of histories of spacetime geometry [GQMST]. In particular it is concerned with the metric's signature. This is evaluated numerically for some simple triangulations of the three-sphere and the three-torus. In the simplest triangulations of the thee-sphere we found that there is one timelike direction with the rest spacelike. For triangulations around flat space of the three-torus we found degeneracies in the simplicial supermetric. The results are compared with the continuum.
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