Description of the bookElectric and magnetic phenomena are omnipresent in modern
life. Their non-quantum aspects are successfully described by
classical electrodynamics (Maxwell's theory). In this book, which
is an outgrowth of a physics graduate course, the fundamental
structure of classical electrodynamics is presented in the form of
six axioms: (1) electric charge conservation, (2) existence of the
Lorentz force, (3) magnetic
ux conservation, (4) localization
of electromagnetic energy-momentum, (5) existence of an electromagnetic
spacetime relation, and (6) splitting of the electric
current in material and external pieces.
The rst four axioms are well-established. For their formulation
an arbitrary 4-dimensional di erentiable manifold is required
which allows for a foliation into 3-dimensional hypersurfaces.
The fth axiom characterizes the environment in which
the electromagnetic eld propagates, namely spacetime with or
without gravitation. The relativistic description of such general
environments remains a research topic of considerable interest.
In particular, it is only in this fth axiom that the metric tensor
of spacetime makes its appearance, thus coupling electromagnetism
and gravitation. The operational interpretation of
the physical notions introduced is stressed throughout. In particular,
the electrodynamics of moving matter is developed ab
initio.
The tool for formulating the theory is the calculus of exterior
di erential forms which is explained in suÆcient detail, including
the corresponding computer algebra programs.
This book presents a fresh and original exposition of the
foundations of classical electrodynamics in the tradition of the
so-called metric-free approach. The reader will win a new outlook
on the interrelationship and the inner working of Maxwell's
equations and their raison d'^etre.
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