Multiple exchange and high-energy fixed-angle scattering

We study fermion scattering in both Abelian and non-Abelian field theories in the high-energy fixed-angle limit to fourth order in the coupling, with an eye to the validity of the "one hard, multiple soft" exchange picture (Schiff approximation) and to the possibility of naive or anomalous scaling behavior for the amplitude. We find that the Schiff approximation is in error and, if perturbation theory is a guide, that scaling behavior is unlikely. We cannot definitely say whether exponentiation will occur.