Relativistic algebra of space-time and algebrodynamics

We consider a manifestly Lorentz-invariant form L of the biquaternion algebra and its generalization to the case of a curved manifold. The conditions of L-differentiability of L-functions are formulated and considered as the primary equations for fundamental fields modeled with such functions. The e...

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Bibliographic Details
Published inGravitation & cosmology Vol. 22; no. 3; pp. 230 - 233
Main Authors Kassandrov, V. V., Rizcallah, J. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2016
Subjects
Astronomy
Astrophysics and Astroparticles
Classical and Quantum Gravitation
Observations and Techniques
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
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Summary:We consider a manifestly Lorentz-invariant form L of the biquaternion algebra and its generalization to the case of a curved manifold. The conditions of L-differentiability of L-functions are formulated and considered as the primary equations for fundamental fields modeled with such functions. The exact form of the effective affine connection induced by L-differentiability equations is obtained for flat and curved manifolds. In the flat case, the integrability conditions of the connection lead to self-duality of the corresponding curvature, thus ensuring that the source-free Maxwell and SL (2,ℂ) Yang-Mills equations hold on the solutions of the L-differentiability equations.
ISSN:0202-2893
1995-0721
DOI:10.1134/S0202289316030087