Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics) [Paperback]

Science proceeds both by discovery and by a process of recasting what has been learned in simpler and clearer form. It is the fruits of this latter process that are presented in CA to GC, though some new mathematical results are also introduced. The authors have succeeded admirably in recasting large areas of intermediate to advanced mathematics in a powerful unified algebraic language of exceptional clarity. The authors show how the traditional languages of complex numbers, quaternions, matrices, vectors, tensors, spinors and differential forms are all subsumed by the elegant language of Clifford algebra, and their calculi by Clifford analysis. Quite apart from the pleasure that the clarity of Clifford algebra/analysis affords, its value also lies in making it easier to understand what has already been discovered, and thus extending the mathematical grasp of the human mind. I have often seen the terms "breakthrough" and "groundbreaking" applied to paltry advances in science, mostly by the innovators themselves, but surely Clifford algebra/analysis is deserving of such an appellation. It has been long in gestation, but its time has come.

In CA to GC, the authors present a tour-de-force of mathematical exposition, the writing displaying the same perspicuity and precision that marks all of Hestenes' writing. While further-refined versions of much of the material of the book can now be downloaded in the form of pdf files from Hestenes' website, this book will go down in history as a classic of unifying mathematical exposition. The university student should begin with the New Foundations for Classical Mechanics book, but CA to GC should be read by every mathematician, physicist and engineering scientist. The reader contemplating learning Clifford algebra/analysis should also take a look at the rapidly growing amount of information online, and at other books on the subject. It is an honor for me to be the first reviewer of this book on Amazon.com.