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This review of classical field theory describes Maxwell´s equations in their integral, directly testable form, and moves on to their local formulation. Includes detailed figures, worked examples, problems and solutions, highlighted special topics and more.

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The book describes Maxwell´s equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell´s equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz´ equation in paraxial approximation relevant for the description of laser beams.

Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein´s equations and the classical tests of general relativity (perihelion precession of Mercury, and light deflection by the sun).

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Textbook features: detailed figures, worked examples, problems and solutions, boxed inserts, highlighted special topics, highlighted important math etc., helpful summaries, appendix, index.

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Maxwell´s Equations.- Symmetries and Covariance of Maxwell´s Equations.- Maxwell Theory as a Classical Field Theory.- Some Applications of Maxwell Theory.- Local Gauge Theories.- Classical Field Theory of Gravitation.

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Florian Scheck

University Mainz

Successful author of German language textbook series (5 volumes)

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