Geometry of Electromagnetic Systems

From highly respected authors in this field, this book is the first to examine the close relationship between the physical phenomena of electromagnetism and the geometry of space and time. It draws on geometrical insights of the author's mathematical research to produce an outstanding work, which will be of interest to all graduate students and researchers in electromagnetic field theory.

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This book is addressed to engineers, applied mathematicians, and physicists involved in the design and analysis of electromagnetic systems. Its chief purpose is to clarify the structure of electromagnetism. It begins with the Faraday-Maxwell insight that in electromagnetism one is faced with an interconnected dynamical system in which space and time are closely linked with physical phenomena. An appropriate basis is given via differential geometry to describe local relationships, via and topology to describe the system. These tools are introduced in the context of Maxwell's equations in the familiar vector notation. Equations are greatly simplified by the geometrical approach, and the geometrical idea of symmetry unifies the various conservation laws. This book clarifies the relationship between fields, potentials, and sources. Links between macroscopic and quantum phenomena are explored from a geometric angle and there is a simple discussion of superconductivity.