عنوان

A brief introduction to dispersion relations :

(Number (ISBN

3030135829

(Number (ISBN

3030135837

(Number (ISBN

9783030135829

(Number (ISBN

9783030135836

Erroneous ISBN

3030135810

Erroneous ISBN

9783030135812

Title Proper

A brief introduction to dispersion relations :

General Material Designation

[Book]

Other Title Information

with modern applications /

First Statement of Responsibility

José Antonio Oller.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2019.

Specific Material Designation and Extent of Item

1 online resource (viii, 141 pages) :

Other Physical Details

illustrations (some color)

Series Title

SpringerBriefs in physics,

ISSN of Series

2191-5423

Text of Note

Includes bibliographical references.

Text of Note

Intro; Contents; Introduction; 1 S and T Matrices. Unitarity; 2 Two-Body Scattering. Partial-Wave Expansion; 3 Crossing. Crossed-Channel Singularities; 4 Important Mathematical Results: Schwarz Reflection Principle, Sugawara-Kanazawa Theorem, and Herglotz Theorem; 5 Exact Dispersion Relations in Quantum Mechanics for the Eigenvalues of the Scattering Kernel; 6 General Results for Two-Meson Scattering in Partial Waves After Neglecting the Crossed-Channel Cuts. N/D Method; 7 Reaching the Unphysical Riemann Sheets. A Nonlinear Integral Equation to Calculate a PWA

Text of Note

17 An Example of Application of Analyticity in the Nuclear Medium: The Nuclear Energy DensityA Numerical Method to Solve the Coupled Linear IEs in Eq. (15.23); References

0

8

Text of Note

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.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030135829

Title

Brief introduction to dispersion relations.

International Standard Book Number

9783030135812

Dispersion relations.

Elementary Particles, Quantum Field Theory.

Mathematical Methods in Physics.

Nuclear Physics, Heavy Ions, Hadrons.

Dispersion relations.

PHM

PHM

SCI051000

Number

Edition

Class number

Oller, José Antonio

Date of Transaction

20200823071145.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y