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DOI:http://dx.doi.org/10.26855/jamc.2022.06.004

On the Quaternion Representation for Octonion Generalization of Lorentz Boosts

Date: May 23,2022 |Hits: 218 Download PDF How to cite this paper

M. Kharinov

St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), 39, 14th Line V.O., St. Petersburg, 199178, Russia.

*Corresponding author: M. Kharinov

Abstract

The paper proposes an approach to the generalization of Lorentz transformations for the real Euclidean spacetime of double dimensions. The approach is based on symmetry considerations. It provides: a) Generalized additive decomposition of a linear operator into self-adjoint (symmetric) and skewsymmetric parts; b) development of the apparatus of non-associative octonions due to the double generalization of the cross vector product for three arguments and eight-dimensional space; c) quaternion representation of Lorentz transformations as a linear combination of spatial rotation and one more orthogonal transformation; d) analytical solution of the eigenvector/eigenvalue problem for the composition of Lorentz boosts, in order to extend the quaternion record of Lorentz boost composition to the octonionic case. In general, our studies are consistent with those of Tevian Dray and Сorinne A. Manogue, but are limited to using only ordinary quaternions and octonions.

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How to cite this paper

On the Quaternion Representation for Octonion Generalization of Lorentz Boosts

How to cite this paper: M. Kharinov. (2022) On the Quaternion Representation for Octonion Generalization of Lorentz Boosts. Journal of Applied Mathematics and Computation6(2), 198-205.

DOI: http://dx.doi.org/10.26855/jamc.2022.06.004

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