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.
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Kassandrov, V.V., Rizcallah, J.A. Relativistic algebra of space-time and algebrodynamics. Gravit. Cosmol. 22, 230–233 (2016). https://doi.org/10.1134/S0202289316030087
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DOI: https://doi.org/10.1134/S0202289316030087