CHAPTER 1 - The Quadratic Form of a Feynman Diagram

Abstract

This chapter discusses the quadratic form of a Feynman diagram. The representation for the contribution of an arbitrary diagram to the scattering matrix is elaborated in the chapter. The chapter presents an assumption where an arbitrary Feynman diagram with n vertices and l internal lines is considered. All lines of the diagram are oriented and external lines point toward the corresponding vertices, while internal lines may point in any direction. The structure of such a graph can be characterized by a matrix E of n rows and l columns. The n vertices and 1 internal lines are enumerated separately. Feynman amplitude A (s, t) it is sufficient to consider the case when each internal line of the diagram corresponds to the scalar propagator (k2v−m2vÝ + (i0)−1). The contribution Iɛ in the perturbation series for the scattering amplitude is always accompanied by the factor g1, …, gn, where gj is the coupling constant associated with the vertex j.