A Brief Introduction to Dispersion Relations

This text offers a brief introduction to the dispersion relations as an approach to calculate  -matrix elements, a formalism that allows one to take advantage of the analytical structure of scattering amplitudes following the basic principles of unitarity and causality. The last part of this introductory treatment is dedicated to the further impact of scattering amplitudes on a variety of processes through final-state interactions. Several possible approaches are discussed such as the Muskhelishvili-Omnes dispersive integral equations and other closed formulae. These different formalisms are then applied in particular to the study of resonances presenting a number of challenging properties. The book ends with a chapter illustrating the use of dispersion relations in the nuclear medium for the evaluation of the energy density in nuclear matter.