The Dirac equation in a non-Riemannian manifold: II. An analysis using an internal local n -dimensional space of the Yang--Mills type

Journal Article · Fri Jun 01 00:00:00 EDT 1990 · Journal of Mathematical Physics (New York); (USA)

DOI:https://doi.org/10.1063/1.528740· OSTI ID:6848129

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 (USA)

The geometrical properties of a flat tangent space-time local to the generalized manifold of the Einstein--Schroedinger nonsymmetric theory, with an internal {ital n}-dimensional space with the SU({ital n}) symmetry group, is developed here. As an application of the theory, a generalized Dirac equation, where the electromagnetic and the Yang--Mills fields are included in a more complex field equation, is then obtained. When the two-dimensional case is considered, the theory can be immediately interpreted through the algebra of quaternions, which, through the Hurwitz theorem, presupposes a generalization of the theory using the algebra of octonions.

• OSTI ID: 6848129
• Journal Information: Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 31:6; ISSN JMAPA; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EINSTEIN-SCHROEDINGER THEORY
ELECTROMAGNETIC FIELDS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
HURWITZ EFFECT
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
RIEMANN SPACE
SPACE
SPACE-TIME
TWO-DIMENSIONAL CALCULATIONS
UNIFIED-FIELD THEORIES
USES
WAVE EQUATIONS
YANG-MILLS THEORY