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A Brief Introduction to Dispersion Relations

With Modern Applications

  • José Antonio Oller
Book

Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Table of contents

  1. Front Matter
    Pages i-viii
  2. José Antonio Oller
    Pages 1-6
  3. José Antonio Oller
    Pages 7-21
  4. José Antonio Oller
    Pages 23-29
  5. José Antonio Oller
    Pages 111-124
  6. Back Matter
    Pages 135-141

About this book

Introduction


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.

Keywords

Unitarity and analycity S-matrix meson scattering and resonances QCD form factors Muskhelishvili-Omnes dispersive integral equations Two-body scattering scattering amplitudes final-state interactions Dispersion relations and resonance

Authors and affiliations

  • José Antonio Oller
    • 1
  1. 1.Departamento de FísicaUniversidad de MurciaMurciaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-13582-9
  • Copyright Information The Author(s), under exclusive licence to Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-030-13581-2
  • Online ISBN 978-3-030-13582-9
  • Series Print ISSN 2191-5423
  • Series Online ISSN 2191-5431
  • Buy this book on publisher's site
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