  Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation
in Euclidean space are considered. It is argued that the complete set of Dirac
matrices is the most appropriate basis to define the partial amplitudes and to
solve numerically the resulting system of equations with realistic interaction
kernels. Other representations can be obtained by performing proper unitary
transformations. A generalization of the iteration method for finding the
energy spectrum of the BS equation is discussed and examples of concrete
calculations are presented. Comparison of relativistic calculations with
available experimental data and with corresponding non relativistic results
together with an analysis of the role of Lorentz boost effects and relativistic
corrections are presented.
  A novel method related to the use of hyperspherical harmonics is considered
for a representation of the vertex functions suitable for numerical
calculations.
