Direct Bethe-Salpeter solutions in Minkowski space

TL;DR

This paper presents a method for directly solving the Bethe-Salpeter equation in Minkowski space, enabling accurate calculations of bound and scattering states, including electromagnetic form factors, with verified current conservation.

Contribution

It introduces a novel approach to solve the Bethe-Salpeter equation in Minkowski space, including for scattering states, and computes the off-mass shell scattering amplitude for the first time.

Findings

First computation of off-mass shell scattering amplitude for spinless particles

Successful calculation of electromagnetic form factors with current conservation

Validated the method for bound and scattering state solutions

Abstract

We review a method to directly solve the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the many singularities which appear in the kernel and propagators. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange was computed for the first time. Using our Minkowski space solutions for the initial (bound) and final (scattering) states, we calculate elastic and transition (bound to scattering state) electromagnetic form factors. The conservation of the transition electromagnetic current J.q=0, verified numerically, confirms the validity of our solutions.