Overview
- Authors:
- José Antonio Oller
Departamento de Física, Universidad de Murcia, Murcia, Spain
Search author on:PubMed Google Scholar
- 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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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.Similar content being viewed by others
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Table of contents (17 chapters)
Front Matter
Pages i-viiiImportant Mathematical Results: Schwarz Reflection Principle, Sugawara–Kanazawa Theorem, and Herglotz Theorem
- José Antonio Oller
Pages 31-38Exact Dispersion Relations in Quantum Mechanics for the Eigenvalues of the Scattering Kernel
- José Antonio Oller
Pages 39-42General Results for Two-Meson Scattering in Partial Waves After Neglecting the Crossed-Channel Cuts.N / D Method
- José Antonio Oller
Pages 43-50Reaching the Unphysical Riemann Sheets. A Nonlinear Integral Equation to Calculate a PWA
- José Antonio Oller
Pages 51-55Final(Initial)-State Interactions. Unitarity and Analyticity Requirements. Watson Final-State Theorem
- José Antonio Oller
Pages 87-91The Omnès Solution. Reasoned Warnings on the Use of the Omnès Function
- José Antonio Oller
Pages 93-102An Example of Application of Analyticity in the Nuclear Medium: The Nuclear Energy Density
- José Antonio Oller
Pages 125-134Back Matter
Pages 135-141
Authors and Affiliations
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.
Accessibility Information
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