  The reformulation of field theory in which self-energy processes are no
longer present [Annals of Physics, {\bf311} (2004), 314.], [ Progr. Theor.
Phys., {\bf 109} (2003), 881.], [Trends in Statistical Physics {\bf 3} (2000),
115.] provides an adequate tool to transform Swinger-Dyson equations into a
kinetic description outside any approximation scheme. Usual approaches in
quantum electrodynamics (QED) are unable to cope with the mechanical momentum
of the electron and replace it by the canonical momentum. The use of that
unphysical momentum is responsible for the divergences that are removed by the
renormalization procedure in the $S$-matrix theory. The connection between
distribution functions in terms of the canonical and those in terms of the
mechanical momentum is now provided by a dressing operator [Annals of Physics,
{\bf314} (2004), 10] that allows the elimination of the above divergences, as
the first steps are illustrated here.
