Nonperturbative calculation of Green and vertex functions in terms of particle contours

Abstract

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.

Comments: LaTeX, using Worldstyle and comprising three eps files (7 pages in total). Invited talk presented at the International Conference Problems of Quantum Field Theory, May 13 - 18, 1996, Alushta, Crimea, Ukraine. To appear in the Proceedings