Foundations of Classical Electrodynamics (Progress in Mathematical Physics)

Features

• Cover Type: Hard Cover with 320 pages
• Published by: Birkhäuser Boston
• Edition: 1st Edition August 7, 2003
• Written in: English
• ISBN 10 Number: 0817642226
• ISBN 13 Number: 978-0817642228
• Book Dimensions: 9.1 x 6.3 x 1.2 inches
• Weighs: 1.4 pounds

Product 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

 

Product Description


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.

Reader Reviews
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.