Electrodynamics: A Modern Geometric Approach (Progress in Physics, Vol 17)

Rating:
Summary: Necessary evil
Review: In the lack of a good books on Geometric algebra and calculus (in David Hestenes' style) for physicists, the book on electrodynamics by W. Baylis looks like a Necessary evil.

The publishers did thier best to make the book at least look good. Unfortunately, the author could do better.

The annoying 'americanisms' and often inappropriate 'pseudo-scientific jargon' did not help the book.

Poor understanding of physics (not saying the geometrica algebra and analysis) is very surprising and unfortunate for the university professor.

However, with some work on the part of the reader, the book could be somewhat useful. A lot of examples and exercises is also helpful.

Highly recommend to compare Mr. Baylis' style with clear and thoughtful style of David Hestenes (see his "New foundations for physics". Unfortunately the price for that is VERY high ~ $250 )

Again, the book could be much better, but in the said vacuum, is a Necessary evil. Buy it ! ( if you have some spare money and not afraid of the strangers with professor titles)

Rating:
Summary: It's about time!
Review: 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.

In this regard, the book by Baylis is a real blessing. By choosing the simplest geometric algebra (complex quaternions, known in quantum mechanics as the Pauli algebra), Baylis manages to use the full power of Clifford algebra without giving up the familiar notation of vector analysis (gradient, curl, divergence). The only new ingredient is the associative product of two vectors, which unifies their inner product and their cross product and leads to tremendous new possibilities. Students and workers in the field will love the resulting beauty and simplicity, and especially the continuity of notation and concepts with the mainstream literature. Although the Pauli algebra is usually associated with nonrelativistic quantum mechanics, Baylis amply demonstrates that it is equally able to handle relativistic aspects (such as the unified electromagnetic field and Lorentz transformations) when the concept of three-dimensional vectors is replaced by four-dimensional (space-time) "paravectors." Well done!