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arXiv · 1009.2811

Semiclassical Mechanics of the Wigner 6j-Symbol

Vincenzo Aquilanti·Hal M. Haggard·Austin Hedeman·Nadir Jeevanjee·Robert G. Littlejohn·Liang Yu
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Abstract

The semiclassical mechanics of the Wigner 6j-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. A generalization of the Yutsis-type of spin network is developed for this purpose. Special attention is devoted to symplectic reduction, the reduced phase space of the 6j-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 9j-symbol.

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Vincenzo Aquilanti, Hal M. Haggard, Austin Hedeman, Nadir Jeevanjee, Robert G. Littlejohn, Liang Yu. 2010-09-14. Semiclassical Mechanics of the Wigner 6j-Symbol. https://doi.org/10.1088/1751-8113/45/6/065209

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