Asymptotics of spinfoam amplitude on simplicial manifold: Lorentzian theory (Q2851403)

This article studies the large \(j\) asymptotics of the Engle-Pereira-Rovelli-Livine vertex for spin foams in the Lorentzian case. The simplicial complex partitions into three regions. One region corresponds to nondegenerate discrete Lorentzian geometry. Another region is associated with a nondegenerate Euclidean geometry and the last region is associated with a vector geometry. The paper labels the last two types as degenerate configurations. The nondegenerate Lorentzian and Euclidean regions are further partitioned according to the sign of the volume. In each of those regions the spinfoam amplitude reproduces the Regge action with a prefactor of the sign of the volume.