A brief introduction to dispersive methods

Abstract: These lectures aim to provide a basic introduction to dispersive methods and their modern applications to the phenomenology of the Standard Model at low energy. This approach exploits analyticity properties of Green functions and scattering amplitude, often combined with unitarity constraints. To find a logically coherent set of topics in this vast subject, I start with the two-point Green's function, show that this needs the three-point function as input which in turn needs the four-point function. The sequence stops here, just like these lectures, because the four-point function is related only to itself (if one ignores inelastic effects), I will discuss these dispersion relations both in the case of toy models, simple scalar theories, as well as in the phenomenologically relevant case of QCD.