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BL
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| Record Number
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858996
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| Main Entry
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Oller, José Antonio
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| Title & Author
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A brief introduction to dispersion relations : : with modern applications /\ José Antonio Oller.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2019.
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| Series Statement
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SpringerBriefs in physics,
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| Page. NO
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1 online resource (viii, 141 pages) :: illustrations (some color)
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| ISBN
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3030135829
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: 3030135837
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: 9783030135829
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: 9783030135836
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3030135810
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9783030135812
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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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
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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
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| Abstract
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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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| Subject
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Dispersion relations.
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| Subject
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Dispersion relations.
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| Subject
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Nuclear Physics, Heavy Ions, Hadrons.
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| Subject
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Elementary Particles, Quantum Field Theory.
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| Subject
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Mathematical Methods in Physics.
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| Dewey Classification
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539.7/5
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| LC Classification
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QC794
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