Introduction to Octonion and Other Non-Associative Algebras in Physics

A book for both physicists and mathematicians dealing with the application of non-associative algebras in physics.

Susumo Okubo (Author)

9780521017923, Cambridge University Press

Paperback, published 22 August 2005

152 pages, 2 b/w illus.
22.9 x 15.1 x 0.9 cm, 0.243 kg

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

In this book, the author aims to familiarise researchers and graduate students, in both physics and mathematics, with the application of non-associative algebras in physics. Topics covered by the author are wide-ranging to include 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 similar subjects. Much of the material found in this book is not available in other standard works. This book will be of interest to graduate students and research scientists in physics and mathematics.

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.

Subject Areas: Physics [PH]