Investigation of Asymptotic Behavior in Field Theory: The Elastic Form Factor

We examine the question whether local relativistic quantum field theory can account for the observed asymptotic behavior of the electromagnetic form factor of the proton. Particular attention is devoted to the theory of pions and nucleons interacting via isospin-symmetric pseudoscalar coupling, with minimal coupling to the electromagnetic field. New techniques are developed for calculating and summing all asymptotically dominant contributions to vertex functions and to propagators from all orders of perturbation theory. The results indicate that summing Feynman graphs in local quantum field theory is unlikely to provide an explanation of the observed rapid decrease of the form factor at large momentum transfers.