Abstract
We derived an asymptotic formula for q-6j symbol. This is a generalization of the former work by Ponzano and Regge. Studying the q-deformed su(2) spin network as a 3-dimensional quantum gravity model, we show that the Turaev-Viro invariant defines naturally regularized path-integral a la Ponzano-Regge in the semi-classical continuum limit. We find a term which should be related to the cosmological constant term in 3-dimensional gravity. The contribution from the cosmological term is effectively included in the pathintegral from the invariant, and the cosmological constant is found to be 4π 2 /k 2 +O(k −4 ), where q 2k =1. We point out also that the duality matrices of the su(2) WZW model may be identified as the Turaev-Viro invariant evaluated on a certain 3-manifold
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