Generalized Sums over Histories for Quantum Gravity II. Simplicial Conifolds

Details Generalized Sums over Histories for Quantum Gravity II. Simplicial Conifolds Generalized Sums over Histories for Quantum Gravity II. Simplicial Conifolds

1993-07-14

arxiv.org/abs/gr-qc/9307019v1

Nucl.Phys. B402 (1993) 469-530

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

82pp., plain TeX, To appear in Nucl. Phys. B,FF-92-2

Scientific paper

10.1016/0550-3213(93)90650-E

This paper examines the issues involved with concretely implementing a sum over conifolds in the formulation of Euclidean sums over histories for gravity. The first step in precisely formulating any sum over topological spaces is that one must have an algorithmically implementable method of generating a list of all spaces in the set to be summed over. This requirement causes well known problems in the formulation of sums over manifolds in four or more dimensions; there is no algorithmic method of determining whether or not a topological space is an n-manifold in five or more dimensions and the issue of whether or not such an algorithm exists is open in four. However, as this paper shows, conifolds are algorithmically decidable in four dimensions. Thus the set of 4-conifolds provides a starting point for a concrete implementation of Euclidean sums over histories in four dimensions. Explicit algorithms for summing over various sets of 4-conifolds are presented in the context of Regge calculus. Postscript figures available via anonymous ftp at black-hole.physics.ubc.ca (137.82.43.40) in file gen2.ps.

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