Quaternions and Biquaternions: Algebra, Geometry and Physical Theories
Abstract
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups of Q-units transformations leaving Q-multiplication rule form-invariant are determined. A series of mathematical and physical applications is offered, among them use of Q-triads as a moveable frame, analysis of Q-spaces families, Q-formulation of Newtonian mechanics in arbitrary rotating frames, and realization of a Q-Relativity model comprising all effects of Special Relativity and admitting description of kinematics of non-inertial motion. A list of "Quaternionic Coincidences" is presented revealing surprising interconnection between basic relations of some physical theories and Q-numbers mathematics.
Cite
@article{arxiv.math-ph/0501055,
title = {Quaternions and Biquaternions: Algebra, Geometry and Physical Theories},
author = {A. P. Yefremov},
journal= {arXiv preprint arXiv:math-ph/0501055},
year = {2007}
}
Comments
17 pages