Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity

Details Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity

1992-08-18

arxiv.org/abs/hep-lat/9208014v1

Commun.Math.Phys. 157 (1993) 93-98

Physics

High Energy Physics

High Energy Physics - Lattice

8 Pages, LaTex, PUPT-1327

Scientific paper

10.1007/BF02098020

Computations in Dynamical Triangulation Models of Four-Dimensional Quantum Gravity involve weighted averaging over sets of all distinct triangulations of compact four-dimensional manifolds. In order to be able to perform such computations one needs an algorithm which for any given $N$ and a given compact four-dimensional manifold $M$ constructs all possible triangulations of $M$ with $\leq N$ simplices. Our first result is that such algorithm does not exist. Then we discuss recursion-theoretic limitations of any algorithm designed to perform approximate calculations of sums over all possible triangulations of a compact four-dimensional manifold.

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