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Asymptotics of relativistic spin networks

John W Barrett and Christopher M Steele

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The stationary phase technique is used to calculate asymptotic formulae for SO(4) relativistic spin networks. For the tetrahedral spin network this gives the square of the Ponzano–Regge asymptotic formula for the SU(2) 6j-symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the spin network evaluation. Finally, we discuss the asymptotics of the SO(3, 1) 10j-symbol.


PACS

04.60.Nc Lattice and discrete methods

02.40.Dr Euclidean and projective geometries

MSC

83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 7 (7 April 2003)

Received 23 October 2002

Published 13 March 2003



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