Physical charged sectors in quantum electrodynamics. I. Infra-red asymptotics

Abstract

The infra-red asymptotic behaviour of the physical charged sectors of quantum electrodynamics is investigated. Properly defined locally gauge-invariant charged fields (nonlocal with respect to the electromagnetic field and different, in nature, from the string variables) are found to have vanishing infra-red anomalous dimension. The corresponding Lehman-Symanzik-Zimmermann limits admit a Fock representation and the Poincare group is implementable on the asymptotic physical Hubert spaces. The scattering matrix is the well known one, but for the fact it admits a representation in which the usual logarithms of the “vanishing photon mass” are substituted by the logarithms of a finite mass scale. The latter is furtherly replaced by the finite energy resolution of the measuring apparatus when cross sections are computed according to the prescription of Bloch and Nordsieck.