Foundations of Classical Electrodynamics

In this book we display the fundamental structure underlying classical electro- dynamics, i. e. , the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More- over, they should be familiar with linear algebra and elementary analysis, in- cluding vector analysis. Some knowledge of differential geometry would help. Our approach rests on the metric-free integral formulation of the conservation laws of electrodynamics in the tradition of F. Kottler (1922), E. Cartan (1923), and D. van Dantzig (1934), and we stress, in particular, the axiomatic point of view. In this manner we are led to an understanding of why the Maxwell equa- tions have their specific form. We hope that our book can be seen in the classical tradition of the book by E. J. Post (1962) on the Formal Structure of Electro- magnetics and of the chapter "e;Charge and Magnetic Flux"e; of the encyclopedia article on classical field theories by C. Truesdell and R. A. Toupin (1960), in- cluding R. A. Toupin's Bressanone lectures (1965); for the exact references see the end of the introduction on page 11. .

In this book we display the fundamental structure underlying classical electro- dynamics, i. e. , the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More- over, they should be familiar with linear algebra and elementary analysis, in- cluding vector analysis. Some knowledge of differential geometry would help. Our approach rests on the metric-free integral formulation of the conservation laws of electrodynamics in the tradition of F. Kottler (1922), E. Cartan (1923), and D. van Dantzig (1934), and we stress, in particular, the axiomatic point of view. In this manner we are led to an understanding of why the Maxwell equa- tions have their specific form. We hope that our book can be seen in the classical tradition of the book by E. J. Post (1962) on the Formal Structure of Electro- magnetics and of the chapter "e;Charge and Magnetic Flux"e; of the encyclopedia article on classical field theories by C. Truesdell and R. A. Toupin (1960), in- cluding R. A. Toupin's Bressanone lectures (1965); for the exact references see the end of the introduction on page 11. .