Dynamical Triangulations, a Gateway to Quantum Gravity ?

Details Dynamical Triangulations, a Gateway to Quantum Gravity ? Dynamical Triangulations, a Gateway to Quantum Gravity ?

1995-03-16

arxiv.org/abs/hep-th/9503108v1

J.Math.Phys. 36 (1995) 6299-6339

Physics

High Energy Physics

High Energy Physics - Theory

Review, 44 pages, tar compressed uuencoded ps-file (after removing header, type csh filename.uu)

Scientific paper

10.1063/1.531246

We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of equivalence classes of metrics. Scaling relations exist and the critical exponents have simple geometric interpretations. Hartle-Hawkings wave functionals as well as reparametrization invariant correlation functions which depend on the geodesic distance can be calculated. The discretized approach makes sense even in higher dimensional space-time. Although analytic solutions are still missing in the higher dimensional case, numerical studies reveal an interesting structure and allow the identification of a fixed point where we can hope to define a genuine non-perturbative theory of four-dimensional quantum gravity.

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