Relativistic algebra of space-time and algebrodynamics
- Authors: Kassandrov V.V.1, Rizcallah J.A.2
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Affiliations:
- Institute of Gravitation and Cosmology
- School of Education
- Issue: Vol 22, No 3 (2016)
- Pages: 230-233
- Section: Article
- URL: https://journals.rcsi.science/0202-2893/article/view/176031
- DOI: https://doi.org/10.1134/S0202289316030087
- ID: 176031
Cite item
Abstract
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.
About the authors
V. V. Kassandrov
Institute of Gravitation and Cosmology
Author for correspondence.
Email: vkassan@sci.pfu.edu.ru
Russian Federation, Moscow
J. A. Rizcallah
School of Education
Email: vkassan@sci.pfu.edu.ru
Lebanon, Beirut