Foundations of Classical Electrodynamics

1. Front Matter

   Pages i-xv

   PDF

2. Introduction

   • Friedrich W. Hehl, Yuri N. Obukhov

   Pages 1-15

3. Mathematics:Some Exterior Calculus

   • Friedrich W. Hehl, Yuri N. Obukhov

   Pages 17-106

4. Axioms of Classical Electrodynamics

   • Friedrich W. Hehl, Yuri N. Obukhov

   Pages 107-191

5. More Mathematics

   • Friedrich W. Hehl, Yuri N. Obukhov

   Pages 193-242

6. The Maxwell-Lorentz Spacetime Relation

   • Friedrich W. Hehl, Yuri N. Obukhov

   Pages 243-311

7. Electrodynamics in Vacuum and in Matter

   • Friedrich W. Hehl, Yuri N. Obukhov

   Pages 313-373

8. Outlook

   • Friedrich W. Hehl, Yuri N. Obukhov

   Pages 375-395

9. Back Matter

   Pages 397-413

   PDF

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 "Charge and Magnetic Flux" 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. .

• Electromagnetism
• Hall effect
• electric current
• electrical engineering
• electromagnetic wave
• gravitation
• magnetism

"[The authors] …have stressed the phenomena underlying the axioms chosen and the operational interpretation of the quantities introduced. In this, they have clearly succeeded."

—Mathematical Reviews

"Throughout this book, the rationalized MKS system of units is used, making analysis more intelligible, and there are many diagrams which are of great help in understanding the text. Each part of the book is followed by a copious list of references.... Also, in appropriate places there are indications how computer algebra (REDUCE/EXCALC) can be used.... The printing and appearance of the book are excellent.... It can be warmly recommended."

—Zentralblatt Math

 

• Institute for Theoretical Physics, University of Cologne, Cologne, Germany

  Friedrich W. Hehl, Yuri N. Obukhov

• Department of Physics & Astronomy, University of Missouri-Columbia, Columbia, USA

  Friedrich W. Hehl

• Department of Theoretical Physics, Moscow State University, Moscow, Russia

  Yuri N. Obukhov

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