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

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 t...

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Bibliographic Details
Published inGravitation & cosmology Vol. 17; no. 1; pp. 1 - 6
Main Author Yefremov, A. P.
Format Journal Article
LanguageEnglish
Published Dordrecht SP MAIK Nauka/Interperiodica 2011
Subjects
Astronomy
Astrophysics and Astroparticles
Classical and Quantum Gravitation
Observations and Techniques
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Spinor Function
Tangent Surface
Tangent Plane
Geometric Image
Interior Structure
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Summary: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.
ISSN:0202-2893
1995-0721
DOI:10.1134/S0202289311010221