The Dirac equation in a non-Riemannian manifold III: An analysis using the algebra of quaternions and octonions

Journal Article · Wed May 01 00:00:00 EDT 1991 · Journal of Mathematical Physics (New York); (USA)

DOI:https://doi.org/10.1063/1.529291· OSTI ID:5711063

Marques-Bonham, S ^[1]

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1. NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, M.S. 209, P.O. Box 500, Batavia, Illinois 60510 (US) Departamento de Campos e Particulas, Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud, 150, 22.290, Rio de Janeiro, RJ, Brazil

The geometrical properties of a flat tangent space-time local to the manifold of the Einstein--Schroedinger nonsymmetric theory to which an internal octonionic space is attached, is developed here. As an application of the theory, an octonionic Dirac equation for a spin-1/2 particle is also obtained, where is now used an octonionic-like gauge field. It is shown that the (quaternionic) nonsymmetric Yang--Mills theory can be easily recovered and from there, the usual gauge theory on a curved space.

• OSTI ID: 5711063
• Journal Information: Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 32:5; ISSN JMAPA; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EINSTEIN-SCHROEDINGER THEORY
EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
RIEMANN SPACE
SPACE
SPACE-TIME
SPINORS
UNIFIED-FIELD THEORIES
USES
WAVE EQUATIONS
YANG-MILLS THEORY