The Geometry and Dynamics of Magnetic Monopoles

The Geometry and Dynamics of Magnetic Monopoles PDF

Author: Michael Francis Atiyah

Publisher: Princeton University Press

Published: 2014-07-14

Total Pages: 143

ISBN-13: 1400859301

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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

Magnetic Monopoles PDF

Author: Yakov M. Shnir

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 534

ISBN-13: 3540290826

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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

Classical Solutions in Quantum Field Theory PDF

Author: Erick J. Weinberg

Publisher: Cambridge University Press

Published: 2012-08-16

Total Pages: 341

ISBN-13: 1139576372

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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)

Macroscopic Electrodynamics: An Introductory Graduate Treatment (Second Edition) PDF

Author: Walter Mark Wilcox

Publisher: World Scientific

Published: 2024-02-08

Total Pages: 967

ISBN-13: 9811275041

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'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.

Essays On The Formal Aspects Of Electromagnetic Theory

Essays On The Formal Aspects Of Electromagnetic Theory PDF

Author: Akhlesh Lakhtakia

Publisher: World Scientific

Published: 1993-06-30

Total Pages: 812

ISBN-13: 9814505846

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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

Differential Geometry and Mathematical Physics PDF

Author: Gerd Rudolph

Publisher: Springer

Published: 2017-03-22

Total Pages: 830

ISBN-13: 9402409599

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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

The Many Facets of Geometry PDF

Author: Nigel J. Hitchin

Publisher: Oxford University Press

Published: 2010-07

Total Pages: 453

ISBN-13: 0199534926

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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)

Topological Foundations Of Electromagnetism (Second Edition) PDF

Author: Terence William Barrett

Publisher: World Scientific

Published: 2022-05-30

Total Pages: 376

ISBN-13: 9811253315

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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.

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