Renormalization group and the infrared behavior of gauge theories

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Abstract
This paper discusses the application of renormalization-group techniques to the study of the near-mass-shell behavior in gauge theories with fermions. We critically review past work for the Abelian theory of quantum electrodynamics (QED), and also summarize what is known from perturbative analysis. We reformulate the renormalization-group equation in a way which is acceptable to the infrared region and discuss the subsidiary requirements necessary to obtain useful results from this equation. Our analysis is cast in a framework which avoids any dependence on the simple group structure of QED and is thus suitable for generalization to the non-Abelian case. A full discussion of that case is reserved for a later paper, but we present here some discussion of the differences which arise and the modifications which they necessitate in our analysis.