Progress in Mathematical Physics

Foundations of Classical Electrodynamics

Charge, Flux, and Metric

Authors: Hehl, Friedrich W., Obukhov, Yuri N.

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About this Textbook

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.

Reviews

"[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

 


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4612-0051-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-0-8176-4222-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA in USD
  • ISBN 978-1-4612-6590-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Foundations of Classical Electrodynamics
Book Subtitle
Charge, Flux, and Metric
Authors
Series Title
Progress in Mathematical Physics
Series Volume
33
Copyright
2003
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0051-2
DOI
10.1007/978-1-4612-0051-2
Hardcover ISBN
978-0-8176-4222-8
Softcover ISBN
978-1-4612-6590-0
Series ISSN
1544-9998
Edition Number
1
Number of Pages
XV, 113
Topics