Introduction to Momentum Space Integration Techniques in Perturbation Theory

Abstract

Generalized ``pinch'' techniques are developed for analyzing singularity configurations of any Feynman integral in the product space of the loop momenta. The Landau equations follow immediately, and the dual diagrams arise naturally as geometric singularity criteria. Cutkosky's formula for the discontinuity is derived by an elementary method, and its structure is clearly exhibited by this approach. The basic differences between Landau and non‐Landau singularities for single loop diagrams are discussed, and it is shown why the presence of non‐Landau singularities, in contrast to those in the Landau scheme, depends on the dimensionality of space.