Semiclassical Limits of Extended Racah Coefficients

Details Semiclassical Limits of Extended Racah Coefficients Semiclassical Limits of Extended Racah Coefficients

1998-07-22

arxiv.org/abs/gr-qc/9807061v2

J.Math.Phys.41:924-943,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex2e - 26 pages, 6 figures. Uses AMS-fonts, AMS-LaTeX, epsf.tex and texdraw. Revised version with improved clarity and addi

Scientific paper

10.1063/1.533171

We explore the geometry and asymptotics of extended Racah coeffecients. The extension is shown to have a simple relationship to the Racah coefficients for the positive discrete unitary representation series of SU(1,1) which is explicitly defined. Moreover, it is found that this extension may be geometrically identified with two types of Lorentzian tetrahedra for which all the faces are timelike. The asymptotic formulae derived for the extension are found to have a similar form to the standard Ponzano-Regge asymptotic formulae for the SU(2) 6j symbol and so should be viable for use in a state sum for three dimensional Lorentzian quantum gravity.

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