Laurent Freidel and David Louapre 2003 Class. Quantum Grav. 20 1267 doi:10.1088/0264-9381/20/7/303
Laurent Freidel1,2 and David Louapre2
Show affiliationsIt 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 behaviour and a way to modify the Barrett–Crane model in order to cure this disease.
83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)
83C27 Lattice gravity, Regge calculus and other discrete methods
Issue 7 (7 April 2003)
Received 8 October 2002, in final form 30 January 2003
Published 10 March 2003
Laurent Freidel and David Louapre 2003 Class. Quantum Grav. 20 1267
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