Asymptotics of 6j and 10j symbols

Details Asymptotics of 6j and 10j symbols Asymptotics of 6j and 10j symbols

2002-09-17

arxiv.org/abs/hep-th/0209134v4

Class.Quant.Grav. 20 (2003) 1267-1294

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 1 figure, factors corrected, presentation improved

Scientific paper

It is well known that the building blocks for state sum models of quantum gravity are given by 6j and 10j symbols. In this work we study the asymptotics of these symbols by using their expressions as group integrals. We carefully describe the measure involved in terms of invariant variables and develop new technics in order to study their asymptotics. Using these technics we compute the asymptotics of the various Euclidean and Lorentzian 6j-symbols. Finally we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating in agreement with a recent result of Baez et al. We discuss the physical origin of this behavior and a way to modify the Barrett-Crane model in order to cure this disease.

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