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Recent attempts to recover the graviton propagator from spin foam modelsinvolve the use of a boundary quantum state peaked on a classical geometry. Thequestion arises whether beyond the case of a single simplex this suffices forpeaking the interior geometry in a semiclassical configuration. In this paperwe explore this issue in the context of quantum Regge calculus with a generaltriangulation. Via a stationary phase approximation, we show that the boundarystate succeeds in peaking the interior in the appropriate configuration, andthat boundary correlations can be computed order by order in an asymptoticexpansion. Further, we show that if we replace at each simplex the exponentialof the Regge action by its cosine -- as expected from the semiclassical limitof spin foam models -- then the contribution from the sign-reversed terms issuppressed in the semiclassical regime and the results match those ofconventional Regge calculus.

Semiclassical regime of Regge calculus and spin foams