High-Energy Behavior of Scattering Amplitudes in Quantum Electrodynamics

Abstract

The perturbation expansion of the elastic electron-electron scattering amplitude is examined in the limit of very high energy and finite momentum transfer (nearly forward scattering). Several classes of graphs involving the exchange of an arbitrary number of virtual photons are summed into an exponential form, but no evidence is found that the exponent contains terms depending logarithmically upon the energy with coefficients varying with the momentum transfer. This leads to the conclusion that the photon is probably not a "Regge pole." Its zero mass and its vector character are seen to be together responsible for this result. A symmetry property of the elastic scattering amplitude shows that terms involving the exchange of an even number of virtual photons do not, in any case, contribute at very high energy in the neighborhood of the forward direction.