Deformation Expression for Elements of Algebras (VIII) --SU(2)-vacuum and the regular representation space--

TL;DR

This paper explores a novel algebraic approach to conceptualize rotations in three-dimensional space without relying on traditional parameters, aiming to provide a more fundamental understanding of rotational motion.

Contribution

It introduces a deformation expression for algebra elements to describe rotations, offering a new algebraic framework for understanding spatial rotations without explicit parameters.

Findings

Develops an algebraic formulation for rotations in ${f R}^3$

Provides a parameter-free description of rotational motion

Connects algebraic structures with geometric rotation concepts

Abstract

Consider the problem "Give the equation of the conceptional rotations in ${\mathbb R}^3$ without using the parameter expressing individual rotations", just as the conceptional motion of constant velocity along straight lines (Galiley motions) is expressed by an elementary differential equation. In this we try to give an answer to the topic related with the above issue.