Semiclassical mechanics of the Wigner 6j symbol

Robert Littlejohn

University of California, Department of Physics, Berkeley, USA

The asymptotics of the Wigner 6j symbol and the Ponzano-Regge formula will be analyzed from the standpoint of the semiclassical mechanics of integrable systems. The 6j symbol is lifted into the phase space of Schwinger oscillators. Nongeneric Lagrangian manifolds appear. They are smooth, compact and connected, but not n-tori. The PR phase is an action integral along these manifolds. Relations between Bargmann and spin coherent states, geometric quantization, and the work of Roberts will be discussed.

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