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Biquaternion Electrodynamics and Weyl-Cartan Geometry of Space-Time

V. V. Kassandrov
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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.

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V. V. Kassandrov. 2000-07-13. Biquaternion Electrodynamics and Weyl-Cartan Geometry of Space-Time. https://arxiv.org/abs/gr-qc/0007027

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