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On the Role of DIV, Jordan & Related...

by Tze C H

Algebraic structures in theoretical physics

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Hardcover New English

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AlbakiReads Editorial

Algebraic structures in theoretical physics

This monograph examines how division algebras—especially quaternions and octonions—and Jordan and related algebras connect with unified theories of fundamental interactions. Its 461 pages survey selected applications across particle physics and other areas of theoretical physics, including Yang–Mills instantons, exceptional broken gauge and supergravity theories, anyonic phenomena, and theories of extended objects in critical dimensions. The subject matter brings abstract algebra into contact with specific frameworks in modern physics, while the volume’s emphasis is primarily on contributions by its authors.

Good fit for readers who enjoy

  • Readers studying algebraic approaches to theoretical or particle physics
  • Researchers interested in quaternions, octonions, Jordan algebras, or their applications in physics

Themes

Division algebras and theoretical physicsJordan and related algebrasUnified interaction theoriesAlgebraic structures in particle physics

Based on publisher information and book metadata.

Book overview

This monograph surveys the role of some associative and non-associative algebras, remarkable by their ubiquitous appearance in contemporary theoretical physics, particularly in particle physics. It concerns the interplay between division algebras, specifically quaternions and octonions, between Jordan and related algebras on the one hand, and unified theories of the basic interactions on the other. Selected applications of these algebraic structures are discussed: quaternion analyticity of Yang-Mills instantons, octonionic aspects of exceptional broken gauge, supergravity theories, division algebras in anyonic phenomena and in theories of extended objects in critical dimensions. The topics presented deal primarily with original contributions by the authors.

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