# Fundamental properties of quaternion spinors

*A.P. Yefremov*^{1}

(1) Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, Russia

### Abstract

The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical meaning as spinor couples and dyads locally describing 2D surfaces. A detailed study of algebraic relationships between the spinor sets belonging to different quaternion units is suggested as an initial step aimed at producing a self-consistent geometric image of spinor-surface distribution on the physical 3D space background.

### References

- A.P.Yefremov, Adv.Sci.Lett., V.3, P. 537-542 (2010).
- W. R. Hamilton, Lectures on Quaternions (Hodges and Smith, Dublin, 1853).
- R. Fueter, Comm. Math. Helv. 4, 9-20 (1932).
- A. P. Yefremov, Lett. Nuovo Cim. 37 (8), 315-316 (1983).
- A. P. Yefremov, F. Smarandache, and V. Christianto, Progress in Physics 3, 42-50 (2007).
- A. P. Yefremov, Six-Dimensional Rotational Relativity, Acta Phys. Hun. 11 (1-2), 147-153 (2000).
- A. P. Yefremov, Adv. Sci. Lett. 1, 179-186 (2008).
- P. Rastall, Rev. Mod. Phys. 2, 820-832 (1964).
- A. P. Yefremov, Hypercomplex Numbers in Geometry and Physics 1, 104-119 (2004).
- A. P. Yefremov, Quaternion Spaces, Frames and Physical Fields (Moscow, RUDN Publ., 2005), p. 41.
- P. Lancaster and M. Tismenetsky, The Theory of Matrices, Second Edition with Applications (Academic Press, San Diego, USA, London, UK, 1985), p. 154.
- A. P. Yefremov, Adv. Sci. Lett. 5, 288-293 (2012).

For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page