Scheck Florian - Classical Field Theory: On Electrodynamics, Non-Abelian Gauge Theories and Gravitation

Schecks successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwells equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwells equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwells theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwells 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 Maxwells 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 Einsteins equations and the classical tests of general relativity.