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Asymptotics of Spinfoam Amplitude on Simplicial Manifold

Nov 22
4:00 pm o'clock to 5:30 pm o'clock
SR 02.729

Asymptotics of Spinfoam Amplitude on Simplicial Manifold We study the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical configurations. Here we show that, given a critical configuration in general, there exists a partition of the simplicial complex into five type of regions, where the regions are simplicial sub-complexes with boundaries. The critical configuration implies different types of geometries in different types of regions, i.e. nondegenerate discrete Lorentzian geometry with positive or negative 4-simplex volume, nondegenerate discrete Euclidean geometry with positive or negative 4-simplex volume, and degenerate vector geometry. At nondegenerate critical points, the spinfoam amplitude gives the Regge action in Lorentzian signature. The Regge action reproduced here contains a sign factor sgn(V_4(v)) of the oriented 4-simplex volume. Therefore the Regge action reproduced here can be viewed a discretized Palatini action with on-shell connection. Finally the asymptotic formula of the spinfoam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.