  Starting with the homogeneous Bethe-Salpeter equation for two fermions, we
perform a 3D reduction using a series expansion around an unspecified
positive-energy instantaneous approximation of the kernel. A second series
expansion is made, at the 3D level, in order to get an "hermitian" potential.
The combination of both series gives a very simple result, which does not
depend of the initial approximation of the kernel anymore, and could be
obtained directly by starting with an approximation of the free propagator. The
generalisation of this result to a system of f (=0,...N) fermions and N-f
bosons is easy.
