Fundamental Properties of Quaternion Spinors

TL;DR

This paper explores the algebraic and geometric properties of quaternion units, revealing their composition from spinor pairs and dyads, and aims to develop a geometric understanding of spinor distributions in 3D space.

Contribution

It introduces a detailed analysis of quaternion units' structure using matrix theory, linking spinors and dyads to geometric surfaces, advancing the understanding of quaternion algebra in physical space.

Findings

Quaternion units are composed of quadratic combinations of spinor pairs.

Spinor sets associated with different quaternion units have specific algebraic relationships.

A framework for visualizing spinor-surface distributions in 3D space is proposed.

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.