  The Bethe-Salpeter equation for two-body bound system with spin $1/2$
constituent is addressed directly in the Minkowski space. In order to
accomplish this aim we use the Nakanishi integral representation of the
Bethe-Salpeter amplitude and exploit the formal tool represented by the exact
projection onto the null-plane. This formal step allows one i) to deal with
end-point singularities one meets and ii) to find stable results, up to
strongly relativistic regimes, that settles in strongly bound systems. We apply
this technique to obtain the numerical dependence of the binding energies upon
the coupling constants and the light-front amplitudes for a fermion-fermion
$0^+$ state with interaction kernels, in ladder approximation, corresponding to
scalar-, pseudoscalar- and vector boson exchanges, respectively. After
completing the numerical survey of the previous cases, we extend our approach
to a quark-antiquark system in $0^-$ state, taking both constituent-fermion and
exchanged boson masses, from lattice calculations. Interestingly, the
calculated light-front amplitudes for such a mock pion show peculiar signatures
of the spin degrees of freedom.
