A Brief Introduction To Dispersion Relations
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Author |
: José Antonio Oller |
Publisher |
: Springer |
Total Pages |
: 142 |
Release |
: 2019-03-22 |
ISBN-10 |
: 9783030135829 |
ISBN-13 |
: 3030135829 |
Rating |
: 4/5 (29 Downloads) |
Synopsis A Brief Introduction to Dispersion Relations by : José Antonio Oller
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.
Author |
: Nussenzveig |
Publisher |
: Academic Press |
Total Pages |
: 449 |
Release |
: 1972-12-15 |
ISBN-10 |
: 9780080956046 |
ISBN-13 |
: 0080956041 |
Rating |
: 4/5 (46 Downloads) |
Synopsis Causality and Dispersion Relations by : Nussenzveig
Causality and Dispersion Relations
Author |
: Vladimir Pascalutsa |
Publisher |
: Morgan & Claypool Publishers |
Total Pages |
: 84 |
Release |
: 2018-07-06 |
ISBN-10 |
: 9781681749198 |
ISBN-13 |
: 168174919X |
Rating |
: 4/5 (98 Downloads) |
Synopsis Causality Rules by : Vladimir Pascalutsa
Scattering of light by light is a fundamental process arising at the quantum level through vacuum fluctuations. This short book will explain how, remarkably enough, this quantum process can entirely be described in terms classical quantities. This description is derived from general principles, such as causality, unitarity, Lorentz, and gauge symmetries. The reader will be introduced into a rigorous formulation of these fundamental concepts, as well as their physical interpretation and applications.
Author |
: Stefan Buhmann |
Publisher |
: Springer |
Total Pages |
: 321 |
Release |
: 2013-02-03 |
ISBN-10 |
: 9783642324666 |
ISBN-13 |
: 3642324665 |
Rating |
: 4/5 (66 Downloads) |
Synopsis Dispersion Forces II by : Stefan Buhmann
In this book, a modern unified theory of dispersion forces on atoms and bodies is presented which covers a broad range of different aspects and scenarios. Macroscopic quantum electrodynamics is applied within the context of dispersion forces. In contrast to the normal-mode quantum electrodynamics traditionally used to study dispersion forces, the new approach allows to consider realistic material properties including absorption and is flexible enough to be applied to a broad range of geometries. Thus general properties of dispersion forces like their non-additivity and the relation between microscopic and macroscopic dispersion forces are discussed. It is demonstrated how the general results can be used to obtain dispersion forces on atoms in the presence of bodies of various shapes and materials. In particular, nontrivial magnetic properties of the bodies, bodies of irregular shapes, the role of material absorption, and dynamical forces for excited atoms are discussed. This volume 2 deals especially with quantum electrodynamics, dispersion forces, Casimir forces, asymptotic power laws, quantum friction and universal scaling laws. The book gives both the specialist and those new to the field a thorough overview over recent results in the context of dispersion forces. It provides a toolbox for studying dispersion forces in various contexts.
Author |
: Peter Moczo |
Publisher |
: Cambridge University Press |
Total Pages |
: 387 |
Release |
: 2014-04-24 |
ISBN-10 |
: 9781139867696 |
ISBN-13 |
: 1139867695 |
Rating |
: 4/5 (96 Downloads) |
Synopsis The Finite-Difference Modelling of Earthquake Motions by : Peter Moczo
Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.
Author |
: Frederick W. Byron |
Publisher |
: Courier Corporation |
Total Pages |
: 674 |
Release |
: 2012-04-26 |
ISBN-10 |
: 9780486135069 |
ISBN-13 |
: 0486135063 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Mathematics of Classical and Quantum Physics by : Frederick W. Byron
Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.
Author |
: Graham W. Griffiths |
Publisher |
: Cambridge University Press |
Total Pages |
: 637 |
Release |
: 2016-04-26 |
ISBN-10 |
: 9781316654156 |
ISBN-13 |
: 131665415X |
Rating |
: 4/5 (56 Downloads) |
Synopsis Numerical Analysis Using R by : Graham W. Griffiths
This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.
Author |
: Hugh Burkhardt |
Publisher |
: |
Total Pages |
: 310 |
Release |
: 1969 |
ISBN-10 |
: UCAL:B3436211 |
ISBN-13 |
: |
Rating |
: 4/5 (11 Downloads) |
Synopsis Dispersion Relation Dynamics by : Hugh Burkhardt
Author |
: A. V. Anisovich |
Publisher |
: World Scientific |
Total Pages |
: 342 |
Release |
: 2013 |
ISBN-10 |
: 9789814478816 |
ISBN-13 |
: 9814478814 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Three-particle Physics and Dispersion Relation Theory by : A. V. Anisovich
The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book.
Author |
: Oliver Bühler |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 178 |
Release |
: 2006 |
ISBN-10 |
: 0821883534 |
ISBN-13 |
: 9780821883532 |
Rating |
: 4/5 (34 Downloads) |
Synopsis A Brief Introduction to Classical, Statistical, and Quantum Mechanics by : Oliver Bühler