The emphasis in this text is on classical electromagnetic theory and electrodynamics, that is, dynamical solutions to the Lorentz force and Maxwell s equations The natural appearance of the Minkowski spacetime metric in the paravector space of Clifford s geometric algebra is used to formulate a covariant treatment in special relativity that seamlessly connects spacetime concepts to the spatial vector treatments common in undergraduate texts Baylis geometrical interpretation, using such powerful tools as spinors and projectors, essentially allows a component free notation and avoids the clutter of indices required in tensorial treatments The exposition is clear and progresses systematically from a discussion of electromagnetic units and an explanation of how the SI system can be readily converted to the Gaussian or natural Heaviside Lorentz systems, to an introduction of geometric algebra and the paravector model of spacetime, and finally, special relativity Other topics include Maxwell s equation s , the Lorentz force law, the Fresnel equations, electromagnetic waves and polarization, wave guides, radiation from accelerating charges and time dependent currents, the Li nard Wiechert potentials, and radiation reaction, all of which benefit from the modern relativistic approach Numerous worked examples and exercises dispersed throughout the text help the reader understand new concepts and facilitate self study of the material Each chapter concludes with a set of problems, many with answers Complete solutions are also available An excellent feature is the integration of Maple into the text, thereby facilitating difficult calculations To download accompanying Maple worksheets, please visit...
|Title||:||Electrodynamics: A Modern Geometric Approach (Progress in Mathematical Physics)|
|Publisher||:||Birkh user Corrected edition January 12, 2004|
|Number of Pages||:||380 pages|
|File Size||:||592 KB|
|Status||:||Available For Download|
|Last checked||:||21 Minutes ago!|
Electrodynamics: A Modern Geometric Approach (Progress in Mathematical Physics) Reviews
If you read research papers on Clifford geometric algebras, you will frequently find this book cited in the references. That, and having run across it accidentally in the library, led me to borrow (later purchase) and read this text as an introduction to Clifford geometric algebras. The book has a great introduction to this material that is not belabored by the "Theorem A, Proposition B" style of mathematical writing; it does rely on some exercises for learning, but they are pretty simple, and I could solve them straightforwardly without much trouble. It focuses on giving you a concise introduction of geometric algebra, and then interprets classical electrodynamics in this language. I came to this book having already a pretty reasonable understanding of electrodynamics as typically taught in graduate school, but wanting to learn a different but equivalent mathematical framework for such a theory. In that sense, this text does excellently.
I quite liked the geometric algebra introduction in this book. It was one of the simplest and clearest I've read. That is, until the paravector notation is introduced. I felt overwhelmed by the variety of conjugation operations suddenly tossed out (clifford conjugation, hermitian conjugation, grade automorphism).
Maxwell's theory of Electrodynamics is considerably more complicated than Newton's Mechanics. The latter deals with concrete objects (particles, rigid bodies, etc.) while the former deals with intangible "fields" distributed in space, a concept that took many years to evolve and gain acceptance. It is therefore not surprising that Electrodynamics has motivated a variety of important scientific developments, designed either to simplify it conceptually or to make it consistent with Mechanics. In physics, fundamental contradictions between Electrodynamics and Mechanics spurred Einstein to develop Special Relativity. In mathematics, the most well-known development is vector analysis, introduced by Gibbs to simplify Maxwell's equations. Unfortunately, the even deeper simplifications introduced by Hamilton (based on quaternions) and Clifford (based on Clifford algebra) have not gained wide acceptance because they are somewhat more technically demanding. Thus almost all physics and engineering textbooks on electrodynamics use vector analysis, and very few students and researchers are even aware of the tremendous power offered by quaternionic and Clifford analysis.
This book on electrodynamics presents an awkward geometric approach.