Nonperturbative Calculation of Green and Vertex Functions in Terms of Particle Contours

The infrared regime of fermionic Green and vertex functions is studied analytically within a geometric approach which simulates soft interactions by an 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.