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We present a method to directly solving the Bethe-Salpeter equation inMinkowski space, both for bound and scattering states. It is based on a propertreatment of the singularities which appear in the kernel, propagators andBethe-Salpeter amplitude itself. The off-mass shell scattering amplitude forspinless particles interacting by a one boson exchange is computed for thefirst time.

Solving Bethe-Salpeter scattering state equation in Minkowski space