Asymptotic analysis of spin foam amplitude with timelike triangles

Understand

The large $j$ asymptotic behavior of $4$-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex.

• We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account.
• The large $j$ asymptotic behavior is determined by critical configurations of the amplitude.
• We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles.