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Book
Causality and dispersion relations
Author:
ISBN: 1282288865 9786612288869 0080956041 0125230508 Year: 1972 Volume: 95 Publisher: New York (N.Y.): Academic press


Book
Three-particle physics and dispersion relation theory
Authors: --- --- --- --- --- et al.
ISBN: 1299462839 9814478814 9789814478816 9814478806 9789814478809 9781299462830 Year: 2013 Publisher: [Hackensack] New Jersey : World Scientific,

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Abstract

The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produc


Book
A Brief Introduction to Dispersion Relations : With Modern Applications
Author:
ISBN: 3030135829 3030135810 Year: 2019 Publisher: Cham : Springer International Publishing : Imprint: Springer,

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Abstract

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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