Semiclassical Mechanics of the Wigner 6j-Symbol
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.
Keywords
Cite
@article{arxiv.1009.2811,
title = {Semiclassical Mechanics of the Wigner 6j-Symbol},
author = {Vincenzo Aquilanti and Hal M. Haggard and Austin Hedeman and Nadir Jeevanjee and Robert G. Littlejohn and Liang Yu},
journal= {arXiv preprint arXiv:1009.2811},
year = {2014}
}
Comments
64 pages, 50 figures