The SAGEX review on scattering amplitudes Chapter 1: Modern fundamentals of amplitudes

This chapter introduces the foundational concepts and techniques for scattering amplitudes. It is meant to be accessible to readers with only a basic understanding of quantum field theory. Topics covered include: the four-dimensional spinor-helicity formalism and the colour decomposition of Yang-Mills scattering amplitudes; the study of soft and collinear limits of Yang-Mills and gravity amplitudes; the BCFW recursion relation and generalised unitarity, also in the superamplitudes formalism of N = 4 supersymmetric Yang-Mills; an overview of standard and hidden symmetries of the S-matrix of N = 4 super symmetric Yang-Mills, such as the conformal, dual conformal and Yangian symmetries; and a brief excursus on form factors of protected and non-protected operators in Yang-Mills theory. Several examples and explicit calculations are also provided.

Automated summary

Scattering amplitudes are important concepts and techniques in quantum field theory. This chapter introduces foundational concepts and techniques, aiming to make readers understand and apply this knowledge.