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Division Algebras: : Octonions Quaternions Complex Numbers and the Algebraic Design of Physics - Geoffrey M. Dixon

Division Algebras:

Octonions Quaternions Complex Numbers and the Algebraic Design of Physics

Hardcover Published: 30th June 1994
ISBN: 9780792328902
Number Of Pages: 238

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The four real division algebras (reals, complexes, quaternions and octonions) are the most obvious signposts to a rich and intricate realm of select and beautiful mathematical structures. Using the new tool of adjoint division algebras, with respect to which the division algebras themselves appear in the role of spinor spaces, some of these structures are developed, including parallelizable spheres, exceptional Lie groups, and triality. In the case of triality the use of adjoint octonions greatly simplifies its investigation. Motivating this work, however, is a strong conviction that the design of our physical reality arises from this select mathematical realm. A compelling case for that conviction is presented, a derivation of the standard model of leptons and quarks.
The book will be of particular interest to particle and high energy theorists, and to applied mathematicians.

Underpinnings
Division Algebra Alone
Tensor Algebras
Connecting to Physics
Spontaneous Symmetry Breaking
10 Dimensions
Doorways
Corridors
Appendices
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792328902
ISBN-10: 0792328906
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 238
Published: 30th June 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 1.91
Weight (kg): 0.48