The KLN Theorem and Soft Radiation in Gauge Theories: Abelian Case

We present a covariant formulation of the Kinoshita, Lee, Nauenberg (KLN) theorem for processes involving the radiation of soft particles. The role of the disconnected diagrams is explored and a rearrangement of the perturbation theory is performed such that the purely disconnected diagrams are factored out. The remaining effect of the disconnected diagrams results in a simple modification of the usual Feynman rules for the S-matrix elements. As an application, we show that when combined with the Low theorem, this leads to a proof of the absense of the $1/Q$ corrections to inclusive processes (like the Drell-Yan process). In this paper the abelian case is discussed to all orders in the coupling.