  The infrared regime of fermionic Green and vertex functions is studied
analytically within a geometric approach which simulates soft interactions by
an {\it effective} theory of contours. Expanding the particle path integral in
terms of dominant contours at large distances, all-order results in the
coupling constant are obtained for the renormalized fermion propagator and a
universal vertex function with physical characteristics close to those
associated with the Isgur-Wise function in the weak decays of heavy mesons. The
extension to the ultraviolet regime is scetched.
