Studies in Field Theory.

This dissertation deals with five studies in field theory which are described in Chapters II to VI. In Chapter II, the infrared behavior of QCD with massless quarks is analyzed. It is pointed out that previous computations are erroneous and it is shown that two-particle inclusive cross-sections with at least one of the incoming particles massless are infrared finite at two loops. Chapter III deals with the analysis of the structure of high-energy inclusive hadron-hadron scattering in the Feynman gauge. It is shown that final state interactions cancel on a graph -by-graph basis after summing over final states, and that the leading high-energy behavior of disconnected parton scatterings in the Feynman gauge is the same as in physical gauges after a sum over gauge invariant sets of graphs. These results justify the use of the Feynman gauge in arguments for factorization of leading-twist cross-sections, and also in the analysis of disconnected multiparton scattering. In Chapter IV, the infrared structure of N = 2 supersymmetric QCD is analyzed. Factorization is verified at leading twist for two-particle inclusive cross-sections. Also it is shown that at higher twist this model behaves differently than ordinary QCD in the sense that uncancelled infrared divergences appear at a lower twist. Chapter V deals with the construction of the full N = 2 supergravity action in terms of N = 1 supergravity and matter N = 1 superfields. It is worthwhile to emphasize the simplicity of this action. Finally, in Chapter VI, the method of projecting extended supersymmetric theories onto N = 1 superspace is applied to the case of the N = 2 supersymmetric abelian vector multiplet coupled to N = 2 supergravity. The constraints are solved in terms of N = 1 unconstrained prepotentials and the complete tensor calculus including the action is presented.