A saddle-point finder and its application to the spin foam model

We introduce a saddle-point finder that can find the complex saddle points for any analytically continued action. We showcase our saddle-point finder by two examples in the EPRL spin foam model: the single vertex case and the case of triangulation ${\mathrm{\Delta }}_3$. In both cases, the complex saddle points are found, and each saddle point’s contribution to the partition function is estimated. We also discuss the geometrical interpretation of each saddle point.