A Modern Introduction to Classical Electrodynamics

Abstract A Modern Introduction to Classical Electrodynamics is suitable for undergraduate students that already had a first exposure to the subject and for graduate students, while more advanced parts makes it a useful resource for PhD students and researchers. The book takes a ‘top-down’ approach, starting from Maxwell’s equations in vacuum and developing systematically and in a logically coherent manner their consequences. Much emphasis is put on the formal structure of the theory. Starting from Maxwell’s equations in vacuum, the central role of gauge invariance and of Special Relativity is emphasised from the beginning. After introductory chapters where are rederived elementary results of electrostatics and magnetostatics, and the multipole expansion, Special Relativity is introduced and most of the subsequent derivations are performed using the covariant formalism and the gauge potentials, allowing for greater conceptual and technical clarity, compared to more traditional treatments. All derivations are performed in great detail. The text also includes advanced topics, such as the field-theoretical treatment of classical electrodynamics or a modern treatment of radiation reaction; these parts are meant for the advanced reader and are clearly marked, and can be skipped without loss of continuity. The second part of the book covers electrodynamics in material media. This includes Maxwell’s equations in material media, frequency dependent response of materials and Kramers-Kronig relations, electromagnetic waves in materials, and scattering of electromagnetic radiation.