Solutions of the Bethe-Salpeter equation in Minkowski space

by J. Carbonell

Thursday 26 Mar 2015, 14:30 → 15:30 Europe/Rome

248 (Building C, first floor)

The solutions of the Bethe-Salpeter equation in Minkoswki space are mandatory for computing some interesting physical quantities like elastic and transition form factors, scattering of-shell amplitudes etc. They are however plagued with the singularities of the free propagators, of the integral kernel and of the amplitude itself making very difficult its numerical computation. This difficulty was overcome in the 50's with use of the "Wick rotation", which transforms the Minkowski into an euclidean metric and allowed to obtain some observables invariant in this transformation. The euclidean Quantum Field Thoery is nowadays a basic ingredient in all the lattice calculations. We will show that this procedure is however not always legitimate - at least in the original framework where its was formulated - without a careful and hopeless knowledge of the analytic structure of the Bethe-Salpeter amplitude in the complex momentum plane. We will present two methods to obtain the first Minkowski solutions for bound and scattering states. The first method is based on the Nakanishi integral transform and the projection of the Bethe-Salpeter equation into the Light Front. A second method is based on a careful analysis of the singularities and provides a direct solution of the original equation. They will be illustrated with the results of the Minkowski amplitudes for bound and scattering states, the electromagnetic elastic and transition form factors in the case of scalar particles interacting by boson exchange kernels.