Customer Reviews

Foundations of Classical Electrodynamics (Progress in Mathematical Physics)

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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.

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.