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Relativistic Electrodynamics and Differential Geometry

Author: Stephen Parrott

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 318

ISBN-13: 1461246849

The aim of this book is to provide a short but complete exposition of the logical structure of classical relativistic electrodynamics written in the language and spirit of coordinate-free differential geometry. The intended audience is primarily mathematicians who want a bare-bones account of the foundations of electrodynamics written in language with which they are familiar and secondarily physicists who may be curious how their old friend looks in the new clothes of the differential-geometric viewpoint which in recent years has become an important language and tool for theoretical physics. This work is not intended to be a textbook in electrodynamics in the usual sense; in particular no applications are treated, and the focus is exclusively the equations of motion of charged particles. Rather, it is hoped that it may serve as a bridge between mathemat ics and physics. Many non-physicists are surprised to learn that the correct equation to describe the motion of a classical charged particle is still a matter of some controversy. The most mentioned candidate is the Lorentz-Dirac equation t . However, it is experimentally unverified, is known to have no physically reasonable solutions in certain circumstances, and its usual derivations raise serious foundational issues. Such difficulties are not extensively discussed in most electrodynamics texts, which quite naturally are oriented toward applying the well-verified part of the subject to con crete problems.

Special Relativity, Electrodynamics, and General Relativity

Author: John B. Kogut

Publisher: Academic Press

Published: 2018-01-09

Total Pages: 454

ISBN-13: 0128137215

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Special Relativity, Electrodynamics, and General Relativity: From Newton to Einstein is intended to teach students of physics, astrophysics, astronomy, and cosmology how to think about special and general relativity in a fundamental but accessible way. Designed to render any reader a "master of relativity, all material on the subject is comprehensible and derivable from first principles. The book emphasizes problem solving, contains abundant problem sets, and is conveniently organized to meet the needs of both student and instructor. Fully revised and expanded second edition with improved figures Enlarged discussion of dynamics and the relativistic version of Newton’s second law Resolves the twin paradox from the principles of special and general relativity Includes new chapters which derive magnetism from relativity and electrostatics Derives Maxwell’s equations from Gauss’ law and the principles of special relativity Includes new chapters on differential geometry, space-time curvature, and the field equations of general relativity Introduces black holes and gravitational waves as illustrations of the principles of general relativity and relates them to the 2015 and 2017 observational discoveries of LIGO

Differential Forms and the Geometry of General Relativity

Author: Tevian Dray

Publisher: CRC Press

Published: 2014-10-20

Total Pages: 315

ISBN-13: 1466510323

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Requiring little more than calculus and some linear algebra, this book provides readers with a coherent path to understanding relativity. It helps readers learn just enough differential geometry to grasp the basics of general relativity. The first half of the book describes some of the surprising implications of relativity without introducing more formalism than necessary. The second half takes a more detailed look at the mathematics of differential forms, showing how they are used to describe key geometric ideas in general relativity.

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Author: Hung Nguyen-Schäfer

Publisher: Springer

Published: 2016-08-16

Total Pages: 389

ISBN-13: 3662484978

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This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.

From Riemann to Differential Geometry and Relativity

Author: Lizhen Ji

Publisher: Springer

Published: 2017-10-03

Total Pages: 647

ISBN-13: 3319600397

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This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

Spacetime

Author: Marcus Kriele

Publisher: Springer Science & Business Media

Published: 1999-10-19

Total Pages: 444

ISBN-13: 3540663770

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This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems. The insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology.

Relativity and Geometry

Author: Roberto Torretti

Publisher: Elsevier

Published: 2014-05-20

Total Pages: 409

ISBN-13: 1483147371

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Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time.

Space, Time, Matter

Author: Hermann Weyl

Publisher: Cosimo, Inc.

Published: 2010-01-01

Total Pages: 352

ISBN-13: 1616404663

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In this classic text first published in German in 1918-this is a translation by HENRY L. BROSE (1890-1965) of the 1921 fourth edition-Weyl considers the role of Euclidean space in physics and the mathematics of Einstein's general theory of relativity, exploring: foundations of affine and metrical geometry conception of n-dimensional geometry tensor algebra the stationary electromagnetic field Riemann's geometry affinely connected manifolds space metrics from the point of view of the Theory of Groups relativistic geometry, kinematics, and optics electrodynamics of moving bodies mechanics of the principle of relativity mass and energy gravitational waves concerning the interconnection of the world as a whole and more.HERMANN KLAUS HUGO WEYL (1885-1955)was a German mathematician who spent most of his life working in Zurich, Switzerland. When the Nazi party began to gain power he fled to a job at the Institute of Advanced Study in Princeton, New Jersey where he continued to develop his representation theory. He was one of the most influential mathematicians of the 20th century. He greatly impacted theoretical physics and number theory and was the first to combine general relativity and electromagnetism

Introduction to Geometry and Relativity

Author: David C. Mello

Publisher: Nova Science Publishers

Published: 2013

Total Pages: 0

ISBN-13: 9781626185425

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This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book. The key features of the book are: Detailed solutions are provided to the Exercises in each chapter; Many of the missing steps that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand; A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area; In its treatment of modern differential geometry, the book employs both a modern, co-ordinate-free approach, and the standard co-ordinate-based approach. This makes the book attractive to a large audience of readers.Also, the book is particularly attractive to professional non-specialists who would like an easy to read introduction to the subject.

Teaching Electromagnetics

Author: Krishnasamy T. Selvan

Publisher: CRC Press

Published: 2021-06-18

Total Pages: 250

ISBN-13: 1000400832

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Teaching Electromagnetics: Innovative Approaches and Pedagogical Strategies is a guide for educators addressing course content and pedagogical methods primarily at the undergraduate level in electromagnetic theory and its applications. Topics include teaching methods, lab experiences and hands-on learning, and course structures that help teachers respond effectively to trends in learning styles and evolving engineering curricula. The book grapples with issues related to the recent worldwide shift to remote teaching. Each chapter begins with a high-level consideration of the topic, reviews previous work and publications, and gives the reader a broad picture of the topic before delving into details. Chapters include specific guidance for those who want to implement the methods and assessment results and evaluation of the effectiveness of the methods. Respecting the limited time available to the average teacher to try new methods, the chapters focus on why an instructor should adopt the methods proposed in it. Topics include virtual laboratories, computer-assisted learning, and MATLAB® tools. The authors also review flipped classrooms and online teaching methods that support remote teaching and learning. The end result should be an impact on the reader represented by improvements to his or her practical teaching methods and curricular approach to electromagnetics education. The book is intended for electrical engineering professors, students, lab instructors, and practicing engineers with an interest in teaching and learning. In summary, this book: Surveys methods and tools for teaching the foundations of wireless communications and electromagnetic theory Presents practical experience and best practices for topical coverage, course sequencing, and content Covers virtual laboratories, computer-assisted learning, and MATLAB tools Reviews flipped classroom and online teaching methods that support remote teaching and learning Helps instructors in RF systems, field theory, and wireless communications bring their teaching practice up to date Dr. Krishnasamy T. Selvan is Professor in the Department of Electronics & Communication Engineering, SSN College of Engineering, since June 2012. Dr. Karl F. Warnick is Professor in the Department of Electrical and Computer Engineering at BYU.