Authors:
- Provides state-of-the-art applications in hadron physics
- Serves as textbook for specialized courses as well as a self-study guide for non specialist researchers
- A self-contained introduction to the vast and rich field of dispersion relations
Part of the book series: SpringerBriefs in Physics (SpringerBriefs in Physics)
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Table of contents (17 chapters)
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Front Matter
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Back Matter
About this book
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.Authors and Affiliations
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Departamento de Física, Universidad de Murcia, Murcia, Spain
José Antonio Oller
About the author
- meson-meson, meson-baryon and nucleon-nucleon production and scattering
- hadron spectroscopy
- heavy quarks
- S-matrix theory
topics on which he has authored more than hundred scientific articles.
Bibliographic Information
Book Title: A Brief Introduction to Dispersion Relations
Book Subtitle: With Modern Applications
Authors: José Antonio Oller
Series Title: SpringerBriefs in Physics
DOI: https://doi.org/10.1007/978-3-030-13582-9
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-13581-2Published: 02 April 2019
eBook ISBN: 978-3-030-13582-9Published: 22 March 2019
Series ISSN: 2191-5423
Series E-ISSN: 2191-5431
Edition Number: 1
Number of Pages: VIII, 141
Number of Illustrations: 9 b/w illustrations, 1 illustrations in colour
Topics: Nuclear Physics, Heavy Ions, Hadrons, Mathematical Methods in Physics, Elementary Particles, Quantum Field Theory