Classical Electrodynamics

This book addresses the theoretical foundations and the main physical consequences of electromagnetic interaction, generally considered to be one of the four fundamental interactions in nature, in a mathematically rigorous yet straightforward way. The major focus is on the unifying features shared by classical electrodynamics and all other fundamental relativistic classical field theories.

The aim of this book is to provide a short but complete exposition of the logical structure of classical relativistic electrodynamics written in the language and spirit of coordinate-free differential geometry. The intended audience is primarily mathematicians who want a bare-bones account of the foundations of electrodynamics written in language with which they are familiar and secondarily physicists who may be curious how their old friend looks in the new clothes of the differential-geometric viewpoint which in recent years has become an important language and tool for theoretical physics.

Mathematical intuition behind Electromagnetism

The bibliography on electromagnetism is very rich and it may be necessary to justify our effort in writing a new text. The present text arose as a need when lecturing about the subject at Instituto Balseiro, in Bariloche, Argentina. We wanted to have a reference text for the most important topics covered in the course, which would also cover some aspects of interest for the applications of the concepts that the students have learned. follows one in classical mechan­ A course on electromagnetism usually ics. In the latter a brief introduction to the theory of relativity is normally included. During courses on electromagnetism this theory is traditionally pre­ sented again in brief form. This approach has the effect that, unless students later work on related topics, they do not acquire an appropriate knowledge of relativity. In this way, they lose perspective of the importance of one of the most beautiful and fascinating creations of physics in the twentieth cen­ tury. For this reason, we consider the properties of charges, currents and electromagnetic fields in vacuum, highlighting the relativistic transformation properties of each quantity.

This book summarizes the basics of electricity and magnetism prior to covariant formulation of Maxwell's equations. The book works out the basics of special relativity and then applies the covariant formalism to understand radiation, both in vacuum and in material medium. The emphasis is on cleaner mathematical formalism based on experimental facts. The book contains many problems/exercises which will help the students to understand the basics of the subject.

Advanced Electromagnetic Theory

This book addresses the theoretical foundations and the main physical consequences of electromagnetic interaction, generally considered to be one of the four fundamental interactions in nature, in a mathematically rigorous yet straightforward way. The major focus is on the unifying features shared by classical electrodynamics and all other fundamental relativistic classical field theories. The book presents a balanced blend of derivations of phenomenological predictions from first principles on the one hand, and concrete applications on the other.