Landau Discriminants

Understand

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles.

• In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram.
• The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution.
• In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation.