Semiclassical mechanics of the Wigner 6<i>j</i>-symbol

Abstract

The semiclassical mechanics of the Wigner 6j-symbol is examined from the\nstandpoint of WKB theory for multidimensional, integrable systems, to explore\nthe geometrical issues surrounding the Ponzano-Regge formula. The relations\namong the methods of Roberts and others for deriving the Ponzano-Regge formula\nare discussed, and a new approach, based on the recoupling of four angular\nmomenta, is presented. A generalization of the Yutsis-type of spin network is\ndeveloped for this purpose. Special attention is devoted to symplectic\nreduction, the reduced phase space of the 6j-symbol (the 2-sphere of Kapovich\nand Millson), and the reduction of Poisson bracket expressions for\nsemiclassical amplitudes. General principles for the semiclassical study of\narbitrary spin networks are laid down; some of these were used in our recent\nderivation of the asymptotic formula for the Wigner 9j-symbol.\n