EAN: 9783030135812

SPRINGERBRIEFS IN PHYSICS A BRIEF INTRODUCTIO...

This text offers a brief introduction to the dispersion relations as an approach to calculate
S-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. First  the
case of two-body scattering is considered and then its contribution to other processes through
final-state interactions is discussed. For two-body scattering amplitudes  the general
expression for a partial-wave amplitude is derived in the approximation where the crossed
channel dynamics is neglected. This is taken as the starting point for many interesting
nonperturbative applications  both in the light and heavy quark sector. Subsequently crossed
channel dynamics is introduced within the equations for calculating the partial-wave
amplitudes. Some applications based on methods that treat crossed-channel dynamics
perturbatively are discussed too.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.

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