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

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

2011-02-03

arxiv.org/abs/1102.0618v1

Grav.Cosmol.17:1-6,2011

Physics

General Physics

7 pages, 1 figure

Scientific paper

10.1134/S0202289311010221

Quaternion (Q-) mathematics formally contains many 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 conic-gearing picture). Fundamental Q-unit-spinor relations are found, revealing the geometric meaning of spinors as Lam\'e coefficients (dyads) locally coupling the base and tangent surfaces.

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