Multivectors And Clifford Algebra In Electrodynamics

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World Scientific, 1 янв. 1989 г. - Всего страниц: 332
Clifford algebras are assuming now an increasing role in theoretical physics. Some of them predominantly larger ones are used in elementary particle theory, especially for a unification of the fundamental interactions. The smaller ones are promoted in more classical domains. This book is intended to demonstrate usefulness of Clifford algebras in classical electrodynamics. Written with a pedagogical aim, it begins with an introductory chapter devoted to multivectors and Clifford algebra for the three-dimensional space. In a later chapter modifications are presented necessary for higher dimension and for the pseudoeuclidean metric of the Minkowski space.Among other advantages one is worth mentioning: Due to a bivectorial description of the magnetic field a notion of force surfaces naturally emerges, which reveals an intimate link between the magnetic field and the electric currents as its sources. Because of the elementary level of presentation, this book can be treated as an introductory course to electromagnetic theory. Numerous illustrations are helpful in visualizing the exposition. Furthermore, each chapter ends with a list of problems which amplify or further illustrate the fundamental arguments.
 

Содержание

Chapter 0 MATHEMATICAL PRELIMINARIES
1
Chapter 1 ELECTROMAGNETIC FIELD
69
Chapter 2 ELECTROMAGNETIC POTENTIALS
114
Chapter 3 CHARGES IN THE ELECTROMAGNETIC FIELD
151
Chapter 4 PLANE ELECTROMAGNETIC FIELDS
172
Chapter 5 VARIOUS KINDS OF ELECTROMAGNETIC WAVES
206
Chapter 6 SPECIAL RELATIVITY
227
Chapter 7 RELATIVITY AND ELECTRODYNAMICS
274
Appendix I BEHAVIOUR OF THE INTEGRAL 133
305
Appendix II THE EXISTENCE OF FORCE SURFACES
307
Appendix III SPECIAL EXAMPLES OF FORCE SURFACES
310
REFERENCES
315
INDEX
317
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