The asymptotic limit of the electron field in QED

Summary

Tho construction of locally gauge-invariant charged fields with vanishing anomalous infra-red dimension is sketched in quantum electrodynamics. These fields are nonlocal with respect to tho electromagnetic field and different, in nature, from the string variables. Moreover, they have Lehman-Symanzik-Zimmermann limit admitting a Fock representation. The Poincaré group is implementahle on the corresponding Fock spaces. The scattering matrix is the well known one, with the improvement that the logarithms of the « vanishing photon mass » are replaced by the logarithms of a finite mass scale. The dependence on this mass scale drops out when cross-sections are computed according to the prescription of Bloch and Nordsieck.