Biquaternion Electrodynamics and Weyl-Cartan Geometry of Space-Time

Abstract

The generalized Cauchy-Riemann equations (GCRE) in biquaternion algebra appear to be Lorentz-invariant. The Laplace equation is in this case replaced by a nonlinear (complexified) eikonal equation. GCRE contain the 2-spinor and the gauge structures, and their integrability conditions take the form of free-source Maxwell and Yang-Mills equations. For the value of electric charge from GCRE only the quantization rule follows, as well as the treatment of Coulomb law as a stereographic map. The equivalent geometrodynamics in a Weyl-Cartan affine space and the conjecture of a complex-quaternion structure of space-time are discussed.

7 pages

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