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The conic-gearing image of a complex number and a spinor-born surface geometry
Ефремов А.П. (Yefremov A.P.) The conic-gearing image of a complex number and a spinor-born surface geometry // Gravitation and Cosmology. 2011. 17(1): 1-6. doi: 10.1134/S0202289311010221

Категории: Исследование, Авторский указатель

The conic-gearing image of a complex number and a spinor-born surface geometry
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Аннотация

Quaternion (Q-) mathematics formally containsmany fragments of physical laws; in particular, the Hamiltonian for the Pauli equation automatically emerges in a space with Q-metric. The eigenfunction method shows that any Q-unit has an interior structure consisting of spinor functions; this helps us to represent any complex number in an orthogonal form associated with a novel geometric image (the conicgearing picture). Fundamental Q-unit-spinor relations are found, revealing the geometric meaning of the spinors as Lamé coefficients (dyads) locally coupling the base and tangent surfaces.

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