Description
The study of singularities of Feynman integrals is a classical problem in scattering amplitudes. Inspired by the work of Gelfand, Kapranov, and Zelevinsky (GKZ) on generalized Euler integrals, we define the principal Landau determinant of a Feynman diagram.
I will illustrate several examples using the package PLD.jl. By means of numerical nonlinear algebra methods, PLD.jl makes it possible to compute components of the Landau singular locus that were previously out of reach. I will also briefly discuss the singularities of an Euler integral in the case of a hyperplane arrangement, which can be applied to the computation of singularities of cosmological correlators. This work is based on joint work with Sebastian Mizera and Simon Telen, and with Saiei Matsubara-Heo.