Classical Field Theory

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Scheck’s textbook offers a comprehensive treatment ideal for a one-semester course, beginning with Maxwell's equations in their integral form before transitioning to their local formulation. The initial chapters cover essential properties, including symmetries and covariance in modern notation. The third chapter focuses on Maxwell's theory as a classical field theory and solutions to the wave equation. Chapter four explores significant applications, such as metamaterials with negative refraction indices and Helmholtz' equation solutions relevant to laser beam descriptions. The fifth chapter discusses non-Abelian gauge theories from a classical, geometric perspective, using Maxwell's theory as a prototype, culminating in an application to the U(2) theory pertinent to electroweak interactions. The final chapter summarizes semi-Riemannian geometry as the foundation for classical gravitation theory, concluding with a discussion on the Schwarzschild solution and classical tests of general relativity. This edition introduces a dual-track approach: a fast track for master's students covering essentials and an intensive track for those seeking in-depth knowledge. Clearly labeled material guides students through their preferred level, with numerous problems and worked examples facilitating successful engagement with Classical Field Theory.