Semi-Classical Limits of Simplicial Quantum Gravity

Details Semi-Classical Limits of Simplicial Quantum Gravity Semi-Classical Limits of Simplicial Quantum Gravity

1993-10-08

arxiv.org/abs/gr-qc/9310016v1

Class.Quant.Grav.11:543-556,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages in Plain TeX, (figures available on request), DAMTP-R93/26

Scientific paper

10.1088/0264-9381/11/3/009

We consider the simplicial state-sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions. We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for $6j$-symbols in terms of this geometry. This extends Ponzano and Regge's similar interpretation for Euclidean geometry. We give a geometric interpretation of the stationary points of this state-sum, by showing that, at these points, the simplicial manifold may be mapped locally into flat Lorentzian or Euclidean space. This lends weight to the interpretation of the state-sum as a path integral, which has solutions corresponding to both Lorentzian and Euclidean gravity in three dimensions.

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