  Actual solutions of the Bethe-Salpeter equation for a two-fermion bound
system are becoming available directly in Minkowski space, by virtue of a novel
technique, based on the so-called Nakanishi integral representation of the
Bethe-Salpeter amplitude and improved by expressing the relevant momenta
through light-front components, i.e. $k^\pm=k^0 \pm k^3$. We solve a crucial
problem that widens the applicability of the method to real situations by
providing an analytically exact treatment of the singularities plaguing the
two-fermion problem in Minkowski space, irrespective of the complexity of the
irreducible Bethe-Salpeter kernel. This paves the way for feasible numerical
investigations of relativistic composite systems, with any spin degrees of
freedom. We present a thorough comparison with existing numerical results,
evaluated in both Minkowski and Euclidean space, fully corroborating our
analytical treatment, as well as fresh light-front amplitudes illustrating the
potentiality of non perturbative calculations performed directly in Minkowski
space.
