The Geometry And Dynamics Of Magnetic Monopoles

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The Geometry and Dynamics of Magnetic Monopoles

Michael Francis Atiyah,Nigel Hitchin
The Geometry and Dynamics of Magnetic Monopoles Book PDF

Author : Michael Francis Atiyah,Nigel Hitchin
Publisher : Princeton University Press
Page : 143 pages
File Size : 45,6 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400859306

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The Geometry and Dynamics of Magnetic Monopoles by Michael Francis Atiyah,Nigel Hitchin Pdf

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

Yakov M. Shnir
Magnetic Monopoles Book PDF

Author : Yakov M. Shnir
Publisher : Springer Science & Business Media
Page : 534 pages
File Size : 48,5 Mb
Release : 2006-03-30
Category : Science
ISBN : 9783540290827

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Magnetic Monopoles by Yakov M. Shnir Pdf

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

Erick J. Weinberg
Classical Solutions in Quantum Field Theory Book PDF

Author : Erick J. Weinberg
Publisher : Cambridge University Press
Page : 341 pages
File Size : 44,6 Mb
Release : 2012-08-16
Category : Science
ISBN : 9781139576376

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Classical Solutions in Quantum Field Theory by Erick J. Weinberg Pdf

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.

Macroscopic Electrodynamics: An Introductory Graduate Treatment (Second Edition)

Walter Mark Wilcox,Christopher P Thron
Macroscopic Electrodynamics An Introductory Graduate Treatment Second Edition Book PDF

Author : Walter Mark Wilcox,Christopher P Thron
Publisher : World Scientific
Page : 967 pages
File Size : 51,5 Mb
Release : 2024-02-08
Category : Science
ISBN : 9789811275043

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Macroscopic Electrodynamics: An Introductory Graduate Treatment (Second Edition) by Walter Mark Wilcox,Christopher P Thron Pdf

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

S. K. Donaldson,C. B. Thomas
Geometry of Low Dimensional Manifolds Volume 1 Gauge Theory and Algebraic Surfaces Book PDF

Author : S. K. Donaldson,C. B. Thomas
Publisher : Cambridge University Press
Page : 277 pages
File Size : 45,5 Mb
Release : 1990
Category : Mathematics
ISBN : 9780521399784

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Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces by S. K. Donaldson,C. B. Thomas Pdf

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.

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

Masahiko Kanai,Tadashi Nagano,Hideki Omori,Yoshiaki Maeda
Geometry And Its Applications Proceedings Of The Workshop In Honor Of Morio Obata Book PDF

Author : Masahiko Kanai,Tadashi Nagano,Hideki Omori,Yoshiaki Maeda
Publisher : World Scientific
Page : 286 pages
File Size : 44,6 Mb
Release : 1993-07-06
Category : Electronic
ISBN : 9789814553803

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Geometry And Its Applications - Proceedings Of The Workshop In Honor Of Morio Obata by Masahiko Kanai,Tadashi Nagano,Hideki Omori,Yoshiaki Maeda Pdf

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.

The Many Facets of Geometry

Nigel J. Hitchin
The Many Facets of Geometry Book PDF

Author : Nigel J. Hitchin
Publisher : Oxford University Press
Page : 453 pages
File Size : 44,7 Mb
Release : 2010-07
Category : Mathematics
ISBN : 9780199534920

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The Many Facets of Geometry by Nigel J. Hitchin Pdf

This title celebrates the academic career of Professor Nigel Hitchin - one of the most influential figures in the field of differential and algebraic geometry.

Differential Geometry and Mathematical Physics

Gerd Rudolph,Matthias Schmidt
Differential Geometry and Mathematical Physics Book PDF

Author : Gerd Rudolph,Matthias Schmidt
Publisher : Springer
Page : 830 pages
File Size : 54,5 Mb
Release : 2017-03-22
Category : Science
ISBN : 9789402409598

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Differential Geometry and Mathematical Physics by Gerd Rudolph,Matthias Schmidt Pdf

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 Floer Memorial Volume

Helmut Hofer,Clifford H. Taubes,Alan Weinstein,Eduard Zehnder
The Floer Memorial Volume Book PDF

Author : Helmut Hofer,Clifford H. Taubes,Alan Weinstein,Eduard Zehnder
Publisher : Birkhäuser
Page : 688 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892179

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The Floer Memorial Volume by Helmut Hofer,Clifford H. Taubes,Alan Weinstein,Eduard Zehnder Pdf

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.

Topological Foundations Of Electromagnetism (Second Edition)

Terence William Barrett
Topological Foundations Of Electromagnetism Second Edition Book PDF

Author : Terence William Barrett
Publisher : World Scientific
Page : 376 pages
File Size : 49,6 Mb
Release : 2022-05-30
Category : Science
ISBN : 9789811253317

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Topological Foundations Of Electromagnetism (Second Edition) by Terence William Barrett Pdf

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.

String-Math 2015

Si Li,Bong H. Lian, Wei Song,Shing-Tung Yau
String Math 2015 Book PDF

Author : Si Li,Bong H. Lian, Wei Song,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 55,9 Mb
Release : 2017-11-28
Category : Algebraic geometry -- Projective and enumerative geometry -- Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
ISBN : 9781470429515

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String-Math 2015 by Si Li,Bong H. Lian, Wei Song,Shing-Tung Yau Pdf

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.

Essays On The Formal Aspects Of Electromagnetic Theory

Akhlesh Lakhtakia
Essays On The Formal Aspects Of Electromagnetic Theory Book PDF

Author : Akhlesh Lakhtakia
Publisher : World Scientific
Page : 812 pages
File Size : 42,6 Mb
Release : 1993-06-30
Category : Technology
ISBN : 9789814505840

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Essays On The Formal Aspects Of Electromagnetic Theory by Akhlesh Lakhtakia Pdf

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.

Algebraic Topology and Its Applications

Gunnar E. Carlsson,Ralph L. Cohen,Wu-Chung Hsiang,John D.S. Jones
Algebraic Topology and Its Applications Book PDF

Author : Gunnar E. Carlsson,Ralph L. Cohen,Wu-Chung Hsiang,John D.S. Jones
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461395263

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Algebraic Topology and Its Applications by Gunnar E. Carlsson,Ralph L. Cohen,Wu-Chung Hsiang,John D.S. Jones Pdf

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

Nicholas Manton,Paul Sutcliffe
Topological Solitons Book PDF

Author : Nicholas Manton,Paul Sutcliffe
Publisher : Cambridge University Press
Page : 507 pages
File Size : 55,6 Mb
Release : 2004-06-10
Category : Science
ISBN : 9781139454698

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Topological Solitons by Nicholas Manton,Paul Sutcliffe Pdf

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.

Geometric Approaches to Differential Equations

Peter J. Vassiliou,Ian G. Lisle
Geometric Approaches to Differential Equations Book PDF

Author : Peter J. Vassiliou,Ian G. Lisle
Publisher : Cambridge University Press
Page : 242 pages
File Size : 51,6 Mb
Release : 2000-03-13
Category : Mathematics
ISBN : 0521775981

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Geometric Approaches to Differential Equations by Peter J. Vassiliou,Ian G. Lisle Pdf

A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.