Relativistic Algebra of Space-Time and Algebrodynamics

Abstract

We consider a manifestly Lorentz invariant form $\mathbb{L}$ of the biquaternion algebra and its generalization to the case of curved manifold. The conditions of $\mathbb{L}$-differentiability of $\mathbb{L}$-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 $\mathbb{L}$-differentiability equations is obtained for the flat and curved cases. In the flat case, the integrability conditions of the latter lead to the self-duality of the corresponding curvature, thus ensuring that the source-free Maxwell and $SL(2,\mathbb{C})$ Yang-Mills equations hold on the solutions of the $\mathbb{L}$-differentiability equations

4 pages, twocolumn

References in corpus (2)

• Singular Sources of Maxwell Fields with Self-Quantized Electric Charge
• Algbrodynamics over complex space and phase extension of the Minkowski geometry