Near mass shell singularities in quantum electrodynamics

The authors discuss the near mass shell infrared behavior of QED by performing an explicit sum over all Feynman diagrams in the eikonal approximation. The infrared singularities of exclusive amplitudes in particular limits ((a) small photon mass or dimension not equal to 4, (b) equal off shell p2sub(i), (c) large momentum transfers) are reviewed as special cases of a general parametric formula. In the parametric representation the infrared singularities always exponentiate. This allows a derivation of simple differential equations for Laplace transforms of the scattering amplitudes. Similar differential equations have been conjectured to hold in QCD and the authors summarize the present evidence regarding this assumption. (Auth.)