Asymptotics of 10j symbols
Abstract
The Riemannian 10j symbols are spin networks that assign an amplitude to each 4simplex in the BarrettCrane model of Riemannian quantum gravity. This amplitude is a function of the areas of the ten faces of the 4simplex, and Barrett and Williams have shown that one contribution to its asymptotics comes from the Regge action for all nondegenerate 4simplices with the specified face areas. However, we show numerically that the dominant contribution comes from degenerate 4simplices. As a consequence, one can compute the asymptotics of the Riemannian 10j symbols by evaluating a 'degenerate spin network', where the rotation group SO(4) is replaced by the Euclidean group of isometries of Bbb R^{3}. We conjecture formulae for the asymptotics of a large class of Riemannian and Lorentzian spin networks in terms of these degenerate spin networks, and check these formulae in some special cases. Among other things, this conjecture implies that the Lorentzian 10j symbols are asymptotic to 1/16 times the Riemannian ones.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2002
 arXiv:
 arXiv:grqc/0208010
 Bibcode:
 2002CQGra..19.6489B
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 25 pages LaTeX with 8 encapsulated Postscript figures. v2 has various clarifications and better page breaks. v3 is the final version, to appear in Classical and Quantum Gravity, and has a few minor corrections and additional references