The study of scattering amplitudes in quantum field theory has a long history, dating back to the analytic S-matrix program of the 1960s. The modern field can trace its origins to the 1980s. At that time, the state of the art of amplitude com-putation was five-gluon scattering at tree level, i.e., the lowest order in perturbation theory. Parke and Taylor famously managed to simplify what were page-long results to a beautiful single-line formula, thus providing the first of many hints for the underlying simplicity of scattering amplitudes in gauge theory. To date, the state of the art has advanced by several loop orders, i.e., to higher orders in the perturbative expansion in the coupling constant. This was made possible by many conceptual advances. Modern approaches often use gauge-invariant building blocks, as opposed to the traditional Feynman diagrams, to organise calculations. Perturbative unitarity made it possible to write down relations that recycle these gauge-invariant building blocks, effectively leading to a recursion, both in the number of particles and in the loop order. This is closely related to a deeper understanding of the analytic structure of scattering amplitudes at loop level. Our lecture notes provide an introduction for anyone wishing to learn more about this fascinating subject.

Scattering Amplitudes in Quantum Field Theory PDF

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