Lectures on Clifford (Geometric) Algebras and Applications

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Product Description

The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics.� This� bird's-eye view of �the �discipline is presented by six of the world's leading experts in the field; it� features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The� book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.

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Lectures on Clifford (Geometric) Algebras and Applications Review

This is a very interesting little book on Clifford algebras and applications. It contains six lectures. The editors have written an appendix where a brief review of existing software for computations with Clifford algebras is also presented.

The first lecture, by the late Professor Pertti Lounesto, is a concise but very clear and pedagogically brilliant introduction to Clifford algebras. A more extensive overview can be found in his book "Clifford Algebras and Spinors" (Cambridge University Press, Cambridge, 2nd ed., 2001).

The second lecture, by Ian Porteous, analyzes the mathematical structure of Clifford algebras for real and complex nondegenerate quadratic spaces of arbitrary rank and signature. The third lecture, by John Ryan, focuses on Clifford analysis. The fifth lecture, by J. M. Selig, explores some applications of Clifford algebras in engineering. Finally, in the sixth (and last) lecture, Thomas Branson explains some applications of Clifford algebras in differential geometry.

However, from my perspective, the fourth lecture by William E. Baylis is the most controversial. In fact, the application of Clifford algebras in physics is too important. The discussion on the merits of the so-called algebra of physical space (APS) over the spacetime algebra (STA) of David Hestenes is biased: the author advocates the use of APS as in his book "Electrodynamics: A Modern Geometric Approach" (Birkh�user, Boston, 1999).

Hestenes' STA is the most clear and efficient framework to deal with relativity: actually, it is the fact that STA can easily display the invariants that makes its superiority as a real Geometric Algebra - not only another Clifford Algebra. Besides, the complex paravectors of APS transform the neat structure of Clifford Algebra into a real mess: the geometric interpretation of complex numbers is based on C as a real algebra - not as a field.

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