Description
I will show the recent work on the asymptotic behavior of spin foam amplitude on simplicial manifold, which are done with Muxin Han. We show that for a critical configuration, we can classify the solution in to different types both in Euclidean and Lorentz model. Therefore the Regge action reproduced here can be viewed as a discretized Palatini action with on-shell connection. The asymptotic formula of the spin foam amplitude is given by a sum of the amplitudes evaluated at all possible critical congurations, which are the products of the amplitudes associated to dierent type of geometries
