› › Solitons In Low Dimensional Sigma Models

Low-dimensional Sigma Models,

Author : W. J. Zakrzewski

Publisher : CRC Press

Page : 312 pages

File Size : 44,35 MB

Release : 1989-06

Category : Art

ISBN :

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Book Description

This book gathers together established ideas and applications of sigma models and presents them together with modern applications to provide a unified and complete view of simple sigma models and the role they play in model building in field theoretical methods in elementary particle physics. The book is written for both mathematicians and physicists and is aimed at graduate students and researchers in theoretical particle physics who are interested in sigma models and those working in the general area of harmonic maps in pure mathematics.



Topological Solitons

Author : Nicholas Manton

Publisher : Cambridge University Press

Page : 507 pages

File Size : 40,33 MB

Release : 2004-06-10

Category : Science

ISBN : 1139454692

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Book Description

Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.





Solitons, Instantons, and Twistors

Author : Maciej Dunajski

Publisher : Oxford University Press, USA

Page : 374 pages

File Size : 10,30 MB

Release : 2010

Category : Language Arts & Disciplines

ISBN : 0198570627

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Book Description

A text aimed at third year undergraduates and graduates in mathematics and physics, presenting elementary twistor theory as a universal technique for solving differential equations in applied mathematics and theoretical physics.



Trends in Soliton Research

Author : L. V. Chen

Publisher : Nova Publishers

Page : 154 pages

File Size : 22,79 MB

Release : 2006

Category : Mathematics

ISBN : 9781594545603

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Book Description

Since their discovery a mere thirty years ago, solitons have been invoked to explain such diverse phenomena as: The long lived 'giant red spot' in the highly turbulent Jovian atmosphere. The famous Fermi-Pasta-Ulam paradox wherein a nonlinearly coupled lattice of particles does not display the expected equipartition of energy among available modes. Covering ion-acoustic waves in a plasma, energy storage and transfer in proteins via the Davydov soliton, and, the propagation of short laser pulses in optical fibres over long distances with negligible shape change, this volume presents important research from around the globe.



Quantum Non-linear Sigma-Models

Author : Sergei V. Ketov

Publisher : Springer Science & Business Media

Page : 429 pages

File Size : 44,21 MB

Release : 2013-03-09

Category : Science

ISBN : 3662041928

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Book Description

This is the first comprehensive presentation of the quantum non-linear sigma-models. The original papers consider in detail geometrical properties and renormalization of a generic non-linear sigma-model, illustrated by explicit multi-loop calculations in perturbation theory.



Topological and Non-Topological Solitons in Scalar Field Theories

Author : Yakov M. Shnir

Publisher : Cambridge University Press

Page : 281 pages

File Size : 23,51 MB

Release : 2018-07-26

Category : Science

ISBN : 1316997154

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Book Description

Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples. These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions. The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level. Providing a comprehensive introduction to the description and construction of solitons, this book is ideal for researchers and graduate students in mathematics and theoretical physics.





Solitons and Chaos

Author : Ioannis Antoniou

Publisher : Springer Science & Business Media

Page : 341 pages

File Size : 36,35 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 3642845703

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Book Description

"Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. An introductory note on eight concepts of integrability has been added as a guide for the uninitiated reader. Both specialists and graduate students will find this update on the state ofthe art useful. Key points: chaos vs. integrability; solitons: theory and applications; dissipative systems; Hamiltonian systems; maps and cascades; direct vs. inverse methods; higher dimensions; Lie groups, Painleve analysis, numerical algorithms; pertubation methods.



Noncommutative Geometry and Physics 2005

Author : Ursula Carow-Watamura

Publisher : World Scientific

Page : 333 pages

File Size : 48,63 MB

Release : 2007

Category : Mathematics

ISBN : 9812704698

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Book Description

Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space?time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address these issues and related topics. The book is accessible to both researchers and graduate students beginning to study this subject.