Introduction to Octonion and Other Non-Associative Algebras in Physics

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In this book, the author aims to familiarize researchers and graduate students in both physics and mathematics with the application of non-associative algebras in physics.Topics covered by the author range from algebras of observables in quantum mechanics, angular momentum and octonions, division algebra, triple-linear products and Yang-Baxter equations. The author also covers non-associative gauge theoretic reformulation of Einstein's general relativity theory and so on. Much of the material found in this book is not available in other standard works.
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Editorial Reviews

Okubo (physics and astronomy, U. of Rochester, NY) explains to researchers and graduate students in both physics and mathematics how non-associative algebras are applied in physics. Among his topics are algebras of observables in quantum mechanics, angular momentum and octonians, division algebra, triple-linear products, and Yang-Baxter equations. He also describes a non-associative gauge theoretic reformulation of Einstein's general relativity theory. A first-year graduate knowledge of quantum mechanics and angular momentum algebra is assumed. The lectures were delivered in April 1990 at the University of Rochester, New York. Annotation c. Book News, Inc., Portland, OR (
From the Publisher
"This book will remain an excellent source for applications of nonassociative algebras in physics for a long time." Hyo C. Myung, Mathematical Reviews
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Product Details

Table of Contents

1 Introduction 1
2 Non-associative algebras 11
3 Hurwitz theorems and octonions 21
4 Para-Hurwitz and pseudo-octonion algebras 40
5 Real division algebras and real Clifford algebra 51
6 Clebsch-Gordan algebras 64
7 Algebra of physical observables 80
8 Triple products and ternary systems 89
9 Non-associative gauge theory 115
10 Concluding remark 130
References 131
Index 135
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