Clifford Algebras and Their Application in Mathematical Physics: Aachen 1996 (Fundamental Theories of Physics, 94) by Volker Dietrich (PDF)

Description

Clifford Algebras continues to be a fast-growing discipline, with ever-increasing applications in many scientific fields. This volume contains the lectures given at the Fourth Conference on Clifford Algebras and their Applications in Mathematical Physics, held at RWTH Aachen in May 1996. The papers represent an excellent survey of the newest developments around Clifford Analysis and its applications to theoretical physics. Audience: This book should appeal to physicists and mathematicians working in areas involving functions of complex variables, associative rings and algebras, integral transforms, operational calculus, partial differential equations, and the mathematics of physics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This volume is an unusually inspired collection of papers by some of the most ingenious researchers in Clifford algebras. Since Clifford algebras and the closely related octonion and division algebras are themselves one of the most inspired and ingenious tools in mathematical physics, the reader of this volume cannot go wrong. It is important that mathematicians and physicists learn about Clifford algebras, regardless of their background. Clifford algebras, like most branches of algebra, have a remarkable simplicity that appeals to the researcher’s intuition, and they also have a rigor and a logical development and categorization which is hard to beat in any other branch of mathematics. Clifford algebra goes one step beyond most algebras except perhaps Lie algebras and Grassmanian/tensor algebras in that it is applicable to geometry and geometric physics to a degree that is difficult to believe. For example, quaternions (a branch of Clifford algebra) are now being applied to aerospace and space exploration, as several important volumes recently published indicate. Chisholm in Great Britain, Pezzaglia in California, Hestenes in Arizona, Bayliss and Ackermann, Okubo, Benn, and numerous others have applied Clifford algebra to quantum theory (including quantum field theory and quantum gravity), general and special relativity,and so on. The algebra itself seems to lead researchers forward with less effort. Unlike vector analysis, which struggles with inner product and cross product formalisms which are hard to manipulate, Clifford algebras have a natural multiplication reminiscent of ordinary multiplication which cuts through most of the “red tape” of theoretical and applied physics. The reader should obtain a copy of every publication on Clifford algebras, octonions, Division Algebras, etc. As I have pointed out in another review, readers with poorer mathematical backgrounds can always hire consultants and even tutors to help them translate these remarkable treasures.

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