Semiclassical limits of simplicial quantum gravity
Oct 13, 199314 pages
Published in:
- Class.Quant.Grav. 11 (1994) 543-556
e-Print:
- gr-qc/9310016 [gr-qc]
Report number:
- DAMTP-R-93-26
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Abstract: (arXiv)
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 -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.- quantum gravity: simplex
- path integral
- dimension: 3
- approximation: semiclassical
- Clebsch-Gordan coefficients
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