%0 Generic %1 Barrett1993 %A Barrett, J. W. %A Foxon, T. J. %D 1993 %K LQG QuantumGravity reggecalculus spinfoam %T Semi-Classical Limits of Simplicial Quantum Gravity %U http://arxiv.org/abs/gr-qc/9310016 %X 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.

@misc{Barrett1993, abstract = { 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. }, added-at = {2009-07-28T20:07:43.000+0200}, author = {Barrett, J. W. and Foxon, T. J.}, biburl = {https://www.bibsonomy.org/bibtex/27933470dd23a3ddae152830daeec8e14/random3f}, description = {Semi-Classical Limits of Simplicial Quantum Gravity}, interhash = {7fbdc35af8791481c13c6ac991487780}, intrahash = {7933470dd23a3ddae152830daeec8e14}, keywords = {LQG QuantumGravity reggecalculus spinfoam}, note = {cite arxiv:gr-qc/9310016 Comment: 14 pages in Plain TeX, (figures available on request), DAMTP-R93/26}, timestamp = {2009-07-28T20:07:43.000+0200}, title = {Semi-Classical Limits of Simplicial Quantum Gravity}, url = {http://arxiv.org/abs/gr-qc/9310016}, year = 1993 }