Introduction to Octonion and Other Non-Associative Algebras in Physics

by Susumo Okubo

Overview

In this book, the author applies non-associative algebras to physics. Okubo covers topics ranging from algebras of observables in quantum mechanics and angular momentum and octonions to division algebra, triple-linear products and YangSHBaxter equations. He also discusses the non-associative gauge theoretic reformulation of Einstein's general relativity theory. Much of the material found in this volume is not available in other works. The book will therefore be of great interest to graduate students and research scientists in physics and mathematics.

Product Details

ISBN-13:	9780521472159
Publisher:	Cambridge University Press
Publication date:	08/03/1995
Series:	Montroll Memorial Lecture Series in Mathematical Physics , #2
Pages:	152
Product dimensions:	6.22(w) x 9.25(h) x 0.71(d)

Table of Contents

1. Introduction; 2. Non-associative algebras; 3. Hurwitz theorems and octonions; 4. Para–Hurwitz and pseudo-octonion algebras; 5. Real division algebras and Clifford algebra; 6. Clebsch–Gordon algebras; 7. Algebra of physical observables; 8. Triple products and ternary systems; 9. Non-associative gauge theory; 10. Concluding remarks.

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 (booknews.com)

Booknews

"This book will remain an excellent source for applications of nonassociative algebras in physics for a long time." Hyo C. Myung, Mathematical Reviews

From the Publisher