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Theory of relativity in quaternion spinors

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Abstract

It is shown that the theory of relativity, apart from the standard format and the comparatively new quaternion formulation, can also be presented in terms of quaternion spinors. Mathematically, the spinor format is fundamental while technically it is primitive since it links transformations of reference frames (including non-inertial frames) with an instant rotation of a unique vector “about itself.” Such a rotation in its turn can be regarded as a reciprocal change of scales of two orthogonal directions on a 2D plane, in general, a complex number valued one. This allows for considering any transformation of relative groups SO(3,ℂ) and SL(2,ℂ) and the localized Lorentz group as a deformations of the fractal (pregeometric) spin surface.

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Authors and Affiliations

  1. Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

    A. P. Yefremov

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  1. A. P. Yefremov
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Correspondence to A. P. Yefremov.

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This issue of the journal is dedicated to the centenary of Prof. K.P. Staniukovich. The paper is prepared within RUDN-University program 5-100.

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Yefremov, A.P. Theory of relativity in quaternion spinors. Gravit. Cosmol. 22, 97–106 (2016). https://doi.org/10.1134/S0202289316020171

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  • DOI: https://doi.org/10.1134/S0202289316020171

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