## Semiclassical Mechanics of the Wigner 6j-symbol

V. Aquilanti, H. M. Haggard, A. Hedeman, N. Jeevanjee, R. G. Littlejohn and L. Yu

*Journal of Physics A: Mathematical and Theoretical* **45** (065209), 2012

The semiclassical mechanics of the Wigner 6*j*-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the methods of Roberts and others for deriving the Ponzano- Regge formula are discussed, and a new approach, based on the recoupling of four angular momenta, is presented. Special attention is devoted to symplectic reduction, the reduced phase space of the 6*j*-symbol (the 2-sphere of Kapovich and Millson), and the reduction of Poisson bracket expressions for semiclassical amplitudes. General principles for the semiclassical study of arbitrary spin networks are laid down; some of these were used in our recent derivation of the asymptotic formula for the Wigner 9*j*-symbol.

DOI: 10.1088/1751-8113/45/6/065209

Full text: AqHaHeJeLiYu6j.pdf