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.Comment: 64 pages, 50 figure
