Topological Solitons

Author: Nicholas Manton,Paul Sutcliffe

Publisher: Cambridge University Press

ISBN: 9781139454698

Category: Science

Page: N.A

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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.

Topological and Non-Topological Solitons in Scalar Field Theories

Author: Yakov M. Shnir

Publisher: Cambridge University Press

ISBN: 1316997154

Category: Science

Page: N.A

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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.

Differential Geometry, Gauge Theories, and Gravity

Author: M. Göckeler,T. Schücker

Publisher: Cambridge University Press

ISBN: 9780521378215

Category: Mathematics

Page: 230

View: 6613

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Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

Supermanifolds

Author: Bryce DeWitt

Publisher: Cambridge University Press

ISBN: 9780521423779

Category: Science

Page: 407

View: 6199

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This updated and expanded second edition of an established text presents a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the superanalogs of all the basic structures of ordinary manifold theory.

Solitons, Instantons, and Twistors

Author: Maciej Dunajski

Publisher: Oxford University Press

ISBN: 0198570627

Category: Mathematics

Page: 359

View: 4589

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The book provides a self-contained and accessible introduction to elementary twistor theory; a technique for solving differential equations in applied mathematics and theoretical physics. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basicdifferential geometry, complex manifold theory and the exterior differential system.

Glimpses of Soliton Theory

The Algebra and Geometry of Nonlinear PDEs

Author: Alex Kasman

Publisher: American Mathematical Soc.

ISBN: 0821852450

Category: Mathematics

Page: 304

View: 8863

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Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass -functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Equation and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make this advanced subject accessible to any undergraduate math major, numerous worked examples and thought-provoking but not overly-difficult exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of the software package Mathematica« to facilitate computation and to animate the solutions under study. This book provides the reader with a unique glimpse of the unity of mathematics and could form the basis for a self-study, one-semester special topics, or "capstone" course.

The Universe in a Helium Droplet

Author: G. E. Volovik

Publisher: Oxford University Press on Demand

ISBN: 0198507828

Category: Foreign Language Study

Page: 509

View: 5535

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There are fundamental relations between three vast areas of physics: particle physics, cosmology and condensed matter physics. The fundamental links between the first two areas, in other words, between micro- and macro-worlds, have been well established. There is a unified system of laws governing the scales from subatomic particles to the Cosmos and this principle is widely exploited in the description of the physics of the early Universe. The main goal of this book is to establish and define the connection of these two fields with condensed matter physics. According to the modern view, elementary particles (electrons, neutrinos, quarks, etc.) are excitations of a more fundamental medium called the quantum vacuum. This is the new 'aether' of the 21st Century. Electromagnetism, gravity, and the fields transferring weak and strong interactions all represent different types of the collective motion of the quantum vacuum. Among the existing condensed matter systems, a quantum liquid called superfluid 3He-A most closely represents the quantum vacuum. Its quasiparticles are very similar to the elementary particles, while the collective modes of the liquid are very similar to electromagnetic and gravitational fields, and the quanta of these collective modes are analogues of photons and gravitons. The fundamental laws of physics, such as the laws of relativity (Lorentz invariance) and gauge invariance, arise when the temperature of the quantum liquid decreases. This book is written for graduate students and researchers in all areas of physics.

Classical Solutions in Quantum Field Theory

Solitons and Instantons in High Energy Physics

Author: Erick J. Weinberg

Publisher: Cambridge University Press

ISBN: 0521114632

Category: Science

Page: 326

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Overview of classical solutions and their consequences in quantum field theory, high energy physics and cosmology for graduates and researchers.

The Physical World

An Inspirational Tour of Fundamental Physics

Author: Nicholas Manton,Nicholas Mee

Publisher: Oxford University Press

ISBN: 0198795939

Category: Science

Page: 608

View: 2339

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"It is over half a century since The Feynman lectures on physics were published. A new authoritative account of fundamental physics covering all branches of the subject is now well overdue. The physical world has been written to satisfy this need."--Back cover.

Quantum Field Theory and Its Macroscopic Manifestations

Boson Condensation, Ordered Patterns, and Topological Defects

Author: Massimo Blasone,Petr Jizba,Giuseppe Vitiello

Publisher: World Scientific

ISBN: 1848162804

Category: Science

Page: 526

View: 622

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This book is a self-contained presentation of the quantum field theory of topological defects created during spontaneous symmetry breakdown phase transitions, with a particular emphasis on phenomenological issues of current interest.

Exact Solutions in Three-Dimensional Gravity

Author: Alberto A. García-Díaz

Publisher: Cambridge University Press

ISBN: 1107147891

Category: Science

Page: 454

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A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravities, and therefore providing graduates and researchers with an invaluable resource on this important topic in gravitational physics.

Analysis And Mathematical Physics

Author: Bullett Shaun,Fearn Tom,Smith Frank

Publisher: World Scientific

ISBN: 1786341018

Category: Mathematics

Page: 248

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This is a concise reference book on analysis and mathematical physics, leading readers from a foundation to advanced level understanding of the topic. This is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as distributions, Fourier transforms and microlocal analysis, C* Algebras, value distribution of meromorphic functions, noncommutative differential geometry, differential geometry and mathematical physics, mathematical problems of general relativity, and special functions of mathematical physics. Analysis and Mathematical Physics is the sixth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Quantum Groups in Two-Dimensional Physics

Author: Cisar Gómez,Martm Ruiz-Altaba,German Sierra

Publisher: Cambridge University Press

ISBN: 9780521020046

Category: Science

Page: 476

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A 1996 introduction to integrability and conformal field theory in two dimensions using quantum groups.

The Theory and Applications of Instanton Calculations

Author: Manu Paranjape

Publisher: Cambridge University Press

ISBN: 1107155479

Category: Science

Page: 326

View: 6882

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This book explains in detail the key concepts, calculations and applications elucidating quantum tunnelling mediated by instantons, using the Feynman path integral.

Xvith International Congress on Mathematical Physics (with Dvd-rom)

Author: Pavel Exner

Publisher: World Scientific

ISBN: 9814304638

Category: Science

Page: 708

View: 7036

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The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.

Hamiltonian Mechanics of Gauge Systems

Author: Lev V. Prokhorov,Sergei V. Shabanov

Publisher: Cambridge University Press

ISBN: 1139500902

Category: Science

Page: N.A

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The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

String Theory: Volume 2, Superstring Theory and Beyond

Author: Joseph Polchinski

Publisher: Cambridge University Press

ISBN: 9781139457415

Category: Science

Page: N.A

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String Theory, first published in 1998, comprises two volumes which provide a comprehensive and pedagogic account of the subject. Volume 2 begins with an introduction to supersymmetric string theories and presents the important advances of recent years. The first three chapters introduce the type I, type II, and heterototic superstring theories and their interactions. The next two chapters present important recent discoveries about strongly coupled strings, beginning with a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and black hole entropy. The final chapters are concerned with four-dimensional string theories, showing how some of the simplest string models connect with previous ideas for unifying the Standard Model. They collect many important results on world-sheet and spacetime symmetries. An appendix summarizes the necessary background on fermions and supersymmetry. An essential text and reference for graduate students and researchers interested in superstring theory.

String-Math 2013

Author: Ron Donagi, Michael R. Douglas,Ljudmila Kamenova,Martin Rocek

Publisher: American Mathematical Soc.

ISBN: 1470410516

Category: Mathematics

Page: 370

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This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory. Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more. This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.

D-Branes

Author: Clifford V. Johnson

Publisher: Cambridge University Press

ISBN: 9780521030052

Category: Science

Page: 548

View: 5489

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D-branes represent a key theoretical tool in the understanding of strongly coupled superstring theory and M-theory. They have led to many striking discoveries, including the precise microphysics underlying the thermodynamic behaviour of certain black holes, and remarkable holographic dualities between large-N gauge theories and gravity. This book provides a self-contained introduction to the technology of D-branes, presenting the recent developments and ideas in a pedagogical manner. It is suitable for use as a textbook in graduate courses on modern string theory and theoretical particle physics, and will also be an indispensable reference for seasoned practitioners. The introductory material is developed by first starting with the main features of string theory needed to get rapidly to grips with D-branes, uncovering further aspects while actually working with D-branes. Many advanced applications are covered, with discussions of open problems which could form the basis for other avenues of research.