Foundations of Classical Electrodynamics (Progress in Mathematical Physics) [Hardcover]

F. W. Hehl (Author), Yuri N. Obukhov (Author)

Book Description

Publication Date: August 7, 2003 | ISBN-10: 0817642226 | ISBN-13: 978-0817642228 | Edition: 1

This book presents a fresh, original exposition of the foundations of classical electrodynamics in the tradition of the so-called metric-free approach. The fundamental structure of classical electrodynamics is described in the form of six axioms: (1) electric charge conservation, (2) existence of the Lorentz force, (3) magnetic flux conservation, (4) localization of electromagnetic energy-momentum, (5) existence of an electromagnetic spacetime relation, and (6) splitting of the electric current into material and external pieces. The first four axioms require an arbitrary 4-dimensional differentiable manifold. The fifth axiom characterizes spacetime as the environment in which the electromagnetic field propagates — a research topic of considerable interest — and in which the metric tensor of spacetime makes its appearance, thus coupling electromagnetism and gravitation. Repeated emphasis is placed on interweaving the mathematical definitions of physical notions and the actual physical measurement procedures. The tool for formulating the theory is the calculus of exterior differential forms, which is explained in sufficient detail, along with the corresponding computer algebra programs. Prerequisites for the reader include a knowledge of elementary electrodynamics (with Maxwell's equations), linear algebra and elementary vector analysis; some knowledge of differential geometry would help. "Foundations of Classical Electrodynamics" unfolds systematically at a level suitable for graduate students and researchers in mathematics, physics, and electrical engineering.

Editorial Reviews

Review

"[The authors] …have stressed the phenomena underlying the axioms chosen and the operational interpretation of the quantities introduced. In this, they have clearly succeeded." —Mathematical Reviews "Throughout this book, the rationalized MKS system of units is used, making analysis more intelligible, and there are many diagrams which are of great help in understanding the text. Each part of the book is followed by a copious list of references.... Also, in appropriate places there are indications how computer algebra (REDUCE/EXCALC) can be used.... The printing and appearance of the book are excellent.... It can be warmly recommended." —Zentralblatt Math  

From the Back Cover

This book presents a fresh, original exposition of the foundations of classical electrodynamics in the tradition of the so-called metric-free approach. The fundamental structure of classical electrodynamics is described in the form of six axioms: (1) electric charge conservation, (2) existence of the Lorentz force, (3) magnetic flux conservation, (4) localization of electromagnetic energy-momentum, (5) existence of an electromagnetic spacetime relation, and (6) splitting of the electric current into material and external pieces. The first four axioms require an arbitrary 4-dimensional differentiable manifold. The fifth axiom characterizes spacetime as the environment in which the electromagnetic field propagates — a research topic of considerable interest — and in which the metric tensor of spacetime makes its appearance, thus coupling electromagnetism and gravitation. Repeated emphasis is placed on interweaving the mathematical definitions of physical notions and the actual physical measurement procedures. The tool for formulating the theory is the calculus of exterior differential forms, which is explained in sufficient detail, along with the corresponding computer algebra programs. Prerequisites for the reader include a knowledge of elementary electrodynamics (with Maxwell's equations), linear algebra and elementary vector analysis; some knowledge of differential geometry would help. Foundations of Classical Electrodynamics unfolds systematically at a level suitable for graduate students and researchers in mathematics, physics, and electrical engineering.

Product Details

• Hardcover: 320 pages
• Publisher: Birkhäuser Boston; 1 edition (August 7, 2003)
• Language: English
• ISBN-10: 0817642226
• ISBN-13: 978-0817642228
• Product Dimensions: 9.5 x 6.4 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,852,126 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

20 of 20 people found the following review helpful:

5.0 out of 5 stars New view on Classical Electrodynamics, January 15, 2005

By 

Prof. Chengmin Zhang (Beijing, China) - See all my reviews

This review is from: Foundations of Classical Electrodynamics (Progress in Mathematical Physics) (Hardcover)

The differential geometric method has been one of the most

fundamental tools for theoretical physicists since its first

introduction into special relativity (general relativity) by Albert

Einstein in 1905 (1915). Later it has been applied to many research

areas, such as fluid mechanics, elastomechanics, thermodynamics, solid

state physics, optics, electromagnetism, quantum field theory, etc.

As a distinctive feature of traditional classical electrodynamics,

this book rests on the metric-free integral formulation of the

conservation laws of electrodynamics as represented by exterior

differential forms. Therefore the book will be of great interest to

graduate students and researchers in mathematics and theoretical

physics who work in field theory and general relativity.

The book consists of five parts; a short list of references and an

author and a subject index are included. Every part ends with a list

of references. The authors begin in Part A, as an introductory

section, with an elementary presentation of exterior differential

forms. The necessary geometric concepts, needed to formulate

classical electrodynamics and gravitational theory in the language of

differential forms, are explained in Part A and in Part C, too. The

axioms of classical electrodynamics, the integral formulations of

electric charge and magnetic flux conservation, are presented in Part

B. Subsequently, the linear connection and the metric are introduced

in Part C. The general framework is completed in Part D by a specific

electrodynamic spacetime relation and in Part E by applying

electrodynamics to moving continua and to rotating and accelerating

observers, for instance.

Moreover, a computer algebra program is introduced in the book in

a simple way, and some cartoon drawings will add to the tedious

mathematics some humor. As to the exposition of the book, we are

impressed by illustrations and diagrams, which support our geometrical

insight. The mathematical abstraction and physical relevance are

displayed neatly and appropriately. It is concise and comprehensive

as an introductory textbook for graduate students and a complete

reference book for researchers.

Thus, there is no doubt that many specialists will be interested

in the book under review. The book proves to be a good scientific

resource for university libraries as well as for graduate students and

researchers working in mathematical physics, field theory, and general

relativity.

20 of 22 people found the following review helpful:

5.0 out of 5 stars A metric-free approach to Classical Electrodynamics., January 4, 2004

By 

Prof C. R. PAIVA "Carlos Paiva" (Lisbon, Portugal) - See all my reviews
(REAL NAME)   

This review is from: Foundations of Classical Electrodynamics (Progress in Mathematical Physics) (Hardcover)

This is, in my opinion, the best book available on the foundations of Classical Electrodynamics. Using differential forms, the authors derive the two Maxwell equations (dF=0, dH=J) from four basic axioms in a metric-free approach. Only when two additional axioms are presented, the standard Maxwell-Lorentz theory in vacuum and in matter is developed by taking into account the metric structure of spacetime. Therefore, this framework allows for an almost trivial transition to the curved spacetime of general relativity. Moreover, the electromagnetic excitation H is considered as a microscopic field - whereas, conventionally, only the electromagnetic field strength F is considered as a truly microscopic field.