Continuum Limit of Quenched QED. Critical Exponents and Anomalous Dimensions

Abstract

Recently, there has been an increased interest in strongly coupled QED. This was motivated by the discovery of an ultraviolet stable fixed point at strong couplings [1]. If this fixed point would turn out to be non — gaussian, then QED would be the first nontrivial nonasymptotically free theory in four dimensions. The importance of such a result would be twofold. First, the old question of the existence of QED would be settled. Of course, this would be the case provided that the low energy limit of the theory actually describes photons and electrons; apriori, there is no reason to assume this. Second, and we feel a more important issue, is its paradigmatic value. Within that context QED, or better the U(1) gauge theory, would be a paradigm for other nonasymptoticaly free theories. Of special interest would be nonabelian gauge theories with many flavors so that at weak couplings beta — function is positive (or vanishing). These theories are at present considered as viable candidates for technicolor unification schemes [2].