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Gravitation and Cosmology

, Volume 17, Issue 1, pp 1–6 | Cite as

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

  • A. P. YefremovEmail author
Article

Abstract

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.

Keywords

Tangent Plane Interior Structure Spinor Function Geometric Image Tangent Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Institute of Gravitation and Cosmology of Peoples’ Friendship University of RussiaMoscowRussia

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