The Geometry And Dynamics Of Magnetic Monopoles

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The Geometry and Dynamics of Magnetic Monopoles

Author : Michael Francis Atiyah
Publisher : Princeton University Press
ISBN 13 : 1400859301
Total Pages : 143 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Geometry and Dynamics of Magnetic Monopoles by : Michael Francis Atiyah

Download or read book The Geometry and Dynamics of Magnetic Monopoles written by Michael Francis Atiyah and published by Princeton University Press. This book was released on 2014-07-14 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems governed by non-linear differential equations are of fundamental importance in all branches of science, but our understanding of them is still extremely limited. In this book a particular system, describing the interaction of magnetic monopoles, is investigated in detail. The use of new geometrical methods produces a reasonably clear picture of the dynamics for slowly moving monopoles. This picture clarifies the important notion of solitons, which has attracted much attention in recent years. The soliton idea bridges the gap between the concepts of "fields" and "particles," and is here explored in a fully three-dimensional context. While the background and motivation for the work comes from physics, the presentation is mathematical. This book is interdisciplinary and addresses concerns of theoretical physicists interested in elementary particles or general relativity and mathematicians working in analysis or geometry. The interaction between geometry and physics through non-linear partial differential equations is now at a very exciting stage, and the book is a contribution to this activity. Originally published in 1988. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Magnetic Monopoles

Author : Yakov M. Shnir
Publisher : Springer Science & Business Media
ISBN 13 : 3540290826
Total Pages : 534 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Magnetic Monopoles by : Yakov M. Shnir

Download or read book Magnetic Monopoles written by Yakov M. Shnir and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the monopole problem on a few different levels, from classical electrodynamics up to N=2 SUSY Yang-Mills theory. and presents a compact, `bird's eye view' on the entire set of problems related with very notion of monopole including actual stand of the problem, related historical remarks and comprehensive bibliography. Presents original results obtained by the author in collaboration with other researches are presented as well as it summarizes the present status of the theory of monopoles and provides an introduction to the field.

Classical Solutions in Quantum Field Theory

Author : Erick J. Weinberg
Publisher : Cambridge University Press
ISBN 13 : 1139576372
Total Pages : 341 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Classical Solutions in Quantum Field Theory by : Erick J. Weinberg

Download or read book Classical Solutions in Quantum Field Theory written by Erick J. Weinberg and published by Cambridge University Press. This book was released on 2012-08-16 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical solutions play an important role in quantum field theory, high-energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang–Mills instantons and on bounce solutions.

Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces

Author : S. K. Donaldson
Publisher : Cambridge University Press
ISBN 13 : 0521399785
Total Pages : 277 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces by : S. K. Donaldson

Download or read book Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces written by S. K. Donaldson and published by Cambridge University Press. This book was released on 1990 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.

Macroscopic Electrodynamics: An Introductory Graduate Treatment (Second Edition)

Author : Walter Mark Wilcox
Publisher : World Scientific
ISBN 13 : 9811275041
Total Pages : 967 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Macroscopic Electrodynamics: An Introductory Graduate Treatment (Second Edition) by : Walter Mark Wilcox

Download or read book Macroscopic Electrodynamics: An Introductory Graduate Treatment (Second Edition) written by Walter Mark Wilcox and published by World Scientific. This book was released on 2024-02-08 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Macroscopic Electrodynamics' (ME) is a comprehensive two-semester introductory graduate level textbook on classical electrodynamics for use in physics and engineering programs. The word 'macroscopic' is intended to indicate both the large-scale nature of the theory, as well as the emphasis placed upon applications of the so-called macroscopic Maxwell equations to idealized media. ME emphasizes principles and practical methods of analysis, which are often presented in fresh and original ways. Illustrative examples are carefully chosen to promote the students' physical intuition, and are worked out in detail to give students a thorough grounding in solution techniques. The style is informal yet mathematically sound, and presumes only a basic familiarity with electrodynamics such as that obtained in a one-semester junior-level undergraduate class.At the end of each chapter, many original problems are provided with illustrations or expanded upon specific sections of the text. The problems are at the heart of the text and are meant to encourage students, develop confidence, and emphasize ideas while avoiding both oversimplification and inordinate calculational difficulties.

Geometry And Its Applications - Proceedings Of The Workshop In Honor Of Morio Obata

Author : Masahiko Kanai
Publisher : World Scientific
ISBN 13 : 9814553808
Total Pages : 286 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Geometry And Its Applications - Proceedings Of The Workshop In Honor Of Morio Obata by : Masahiko Kanai

Download or read book Geometry And Its Applications - Proceedings Of The Workshop In Honor Of Morio Obata written by Masahiko Kanai and published by World Scientific. This book was released on 1993-07-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honour of the 65th birthday of Professor M Obata a workshop was held at Keio University. This volume includes notes on the talks and discussions which took place and cover a wide range of subjects on geometry, global analysis, topology and mathematical physics.

Essays On The Formal Aspects Of Electromagnetic Theory

Author : Akhlesh Lakhtakia
Publisher : World Scientific
ISBN 13 : 9814505846
Total Pages : 812 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Essays On The Formal Aspects Of Electromagnetic Theory by : Akhlesh Lakhtakia

Download or read book Essays On The Formal Aspects Of Electromagnetic Theory written by Akhlesh Lakhtakia and published by World Scientific. This book was released on 1993-06-30 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with formal aspects of electromagnetic theory from the classical, the semiclassical and the quantum viewpoints in essays written by internationally distinguished scholars from several countries. The fundamental basis of electromagnetic theory is examined in order to elucidate Maxwell's equations, identify problematic aspects as well as outstanding problems, suggest ways and means of overcoming the obstacles, and review existing literature.This book will be especially valuable for those who wish to go in depth, rather than simply use Maxwell's equations for the solution of engineering problems. Graduate students will find it rich in dissertation topics, and advanced researchers will relish the controversial and detailed arguments and models.

Differential Geometry and Mathematical Physics

Author : Gerd Rudolph
Publisher : Springer
ISBN 13 : 9402409599
Total Pages : 830 pages
Book Rating : 4.4/5 (24 download)

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Book Synopsis Differential Geometry and Mathematical Physics by : Gerd Rudolph

Download or read book Differential Geometry and Mathematical Physics written by Gerd Rudolph and published by Springer. This book was released on 2017-03-22 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory.The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.

The Many Facets of Geometry

Author : Nigel J. Hitchin
Publisher : Oxford University Press
ISBN 13 : 0199534926
Total Pages : 453 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis The Many Facets of Geometry by : Nigel J. Hitchin

Download or read book The Many Facets of Geometry written by Nigel J. Hitchin and published by Oxford University Press. This book was released on 2010-07 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title celebrates the academic career of Professor Nigel Hitchin - one of the most influential figures in the field of differential and algebraic geometry.

Topological Foundations Of Electromagnetism (Second Edition)

Author : Terence William Barrett
Publisher : World Scientific
ISBN 13 : 9811253315
Total Pages : 376 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Topological Foundations Of Electromagnetism (Second Edition) by : Terence William Barrett

Download or read book Topological Foundations Of Electromagnetism (Second Edition) written by Terence William Barrett and published by World Scientific. This book was released on 2022-05-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aims of the book are: (1) to extend Maxwell theory to non-Abelian group forms; (2) to demonstrate that the foundations of electromagnetism are topological; (3) to show the multi-disciplinary nature of communications; (4) to demonstrate the effectiveness of modulated signals in penetrating media; (5) to demonstrate that geometric (Clifford) algebra is the appropriate algebra describing modulated signals.The book is important in indicating that the classical theory of electromagnetism, or Maxwell theory, can be developed to address situations and signals of differing symmetry form, and that different topological spaces require that development.

The Floer Memorial Volume

Author : Helmut Hofer
Publisher : Birkhäuser
ISBN 13 : 3034892179
Total Pages : 688 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Floer Memorial Volume by : Helmut Hofer

Download or read book The Floer Memorial Volume written by Helmut Hofer and published by Birkhäuser. This book was released on 2012-12-06 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, Yang-Mills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder.

String-Math 2015

Author : Si Li
Publisher : American Mathematical Soc.
ISBN 13 : 1470429519
Total Pages : 297 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis String-Math 2015 by : Si Li

Download or read book String-Math 2015 written by Si Li and published by American Mathematical Soc.. This book was released on 2017-11-28 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference String-Math 2015, which was held from December 31, 2015–January 4, 2016, at Tsinghua Sanya International Mathematics Forum in Sanya, China. Two of the main themes of this volume are frontier research on Calabi-Yau manifolds and mirror symmetry and the development of non-perturbative methods in supersymmetric gauge theories. The articles present state-of-the-art developments in these topics. String theory is a broad subject, which has profound connections with broad branches of modern mathematics. In the last decades, the prosperous interaction built upon the joint efforts from both mathematicians and physicists has given rise to marvelous deep results in supersymmetric gauge theory, topological string, M-theory and duality on the physics side, as well as in algebraic geometry, differential geometry, algebraic topology, representation theory and number theory on the mathematics side.

Geometric Approaches to Differential Equations

Author : Peter J. Vassiliou
Publisher : Cambridge University Press
ISBN 13 : 9780521775984
Total Pages : 242 pages
Book Rating : 4.7/5 (759 download)

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Book Synopsis Geometric Approaches to Differential Equations by : Peter J. Vassiliou

Download or read book Geometric Approaches to Differential Equations written by Peter J. Vassiliou and published by Cambridge University Press. This book was released on 2000-03-13 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.

Algebraic Topology and Its Applications

Author : Gunnar E. Carlsson
Publisher : Springer Science & Business Media
ISBN 13 : 1461395267
Total Pages : 271 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Algebraic Topology and Its Applications by : Gunnar E. Carlsson

Download or read book Algebraic Topology and Its Applications written by Gunnar E. Carlsson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications. The main areas of concentration were homotopy theory, K-theory, and applications to geometric topology, gauge theory, and moduli spaces. Workshops were conducted in these three areas. This volume consists of invited, expository articles on the topics studied during this program. They describe recent advances and point to possible new directions. They should prove to be useful references for researchers in Algebraic Topology and related fields, as well as to graduate students.

Topological Solitons

Author : Nicholas Manton
Publisher : Cambridge University Press
ISBN 13 : 1139454692
Total Pages : 507 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Topological Solitons by : Nicholas Manton

Download or read book Topological Solitons written by Nicholas Manton and published by Cambridge University Press. This book was released on 2004-06-10 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Special Metrics and Group Actions in Geometry

Author : Simon G. Chiossi
Publisher : Springer
ISBN 13 : 3319675192
Total Pages : 338 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Special Metrics and Group Actions in Geometry by : Simon G. Chiossi

Download or read book Special Metrics and Group Actions in Geometry written by Simon G. Chiossi and published by Springer. This book was released on 2017-11-27 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Geometric Invariant Theory

Author : David Mumford
Publisher : Springer Science & Business Media
ISBN 13 : 9783540569633
Total Pages : 314 pages
Book Rating : 4.5/5 (696 download)

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Book Synopsis Geometric Invariant Theory by : David Mumford

Download or read book Geometric Invariant Theory written by David Mumford and published by Springer Science & Business Media. This book was released on 1994 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.