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Author: José Antonio Oller Publisher: Springer ISBN: 3030135829 Category : Science Languages : en Pages : 142
Book Description
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: José Antonio Oller Publisher: Springer ISBN: 3030135829 Category : Science Languages : en Pages : 142
Book Description
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: A V Anisovich Publisher: World Scientific ISBN: 9814478822 Category : Science Languages : en Pages : 342
Book Description
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: Vladimir Pascalutsa Publisher: Morgan & Claypool Publishers ISBN: 168174919X Category : Science Languages : en Pages : 84
Book Description
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: Mark N. Berdichevsky Publisher: Springer Science & Business Media ISBN: 3540778144 Category : Science Languages : en Pages : 576
Book Description
Magnetotellurics is finding increasing applications for imaging electrically conductive structures below the Earth`s surface - in both industrial and academic research projects. In this book the authors provide a systematic approach to understanding the modern theory of ill-posed problems which is essential to making confident meaningful interpretations of magnetotelluric and magnetovariational soundings. The interpretation is conducted in an interactive way.
Author: Harold Cohen Publisher: Springer Science & Business Media ISBN: 0387730575 Category : Mathematics Languages : en Pages : 487
Book Description
The Second Edition of this acclaimed text helps you apply theory to real-world applications in mathematics, physics, and engineering. It easily guides you through complex analysis with its excellent coverage of topics such as series, residues, and the evaluation of integrals; multi-valued functions; conformal mapping; dispersion relations; and analytic continuation. Worked examples plus a large number of assigned problems help you understand how to apply complex concepts and build your own skills by putting them into practice. This edition features many new problems, revised sections, and an entirely new chapter on analytic continuation.
Author: Kai-Erik Peiponen Publisher: Springer Science & Business Media ISBN: 9783540645221 Category : Technology & Engineering Languages : en Pages : 152
Book Description
This book is devoted to dispersion theory in linear and nonlinear optics. Dispersion relations and methods of analysis in optical spectroscopy are derived with the aid of complex analysis. The book introduces the mathematical basis and derivations of various dispersion relations that are used in optical spectroscopy. In addition, it presents the dispersion theory of the nonlinear optical processes which are essential in modern optical spectroscopy. The book includes new methods such as the maximum entropy model for wavelength-dependent spectra analysis.
Author: N. D. Hari Dass Publisher: Springer Nature ISBN: 3031353587 Category : Science Languages : en Pages : 468
Book Description
This book presents the essentials culminating in the effective string theory of flux tubes in meticulous technical and conceptual detail. The book is divided into four parts. Part One provides historical background, while Part Two (consisting of 14 chapters) covers the passage from Heisenberg's S-matrix theory to String Theory. This includes non-perturbative LSZ formalism, dispersion relations, Regge poles, duality and dual resonance models. Part Three offers a comprehensive analysis of QCD, focusing on important concepts like asymptotic freedom and quark confinement. The section also delves into lattice gauge theories and effective descriptions of superconductivity and strong interactions. Part Four, the final two chapters, describe the lattice gauge theory determinations of Yang-Mills flux tubes in three and four dimensions and effective string theories, including their systematic constructions. These chapters provide detailed technical information to help readers, especially students, develop their expertise in these ideas. This book is ideal for graduate students, postdocs, and senior researchers looking to deepen their understanding of effective string theory and related concepts.
Author: José Antonio Oller
Author: José Antonio Oller
Author: Nussenzveig
Author: A V Anisovich
Author: Vladimir Pascalutsa
Author: Mark N. Berdichevsky
Author: Harold Cohen
Author: Kai-Erik Peiponen
Author: 
Author: N. D. Hari Dass
Author: United States. National Aeronautics and Space Administration