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

Abstract

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 ${\Delta }_3$. 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.

27 pages, 4 figures

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