Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators

TL;DR

This paper explores the use of quaternions and octonions to systematically analyze SU(2) and SU(3) flavor symmetries, including their generators, commutation relations, and Casimir operators.

Contribution

It introduces a quaternion and octonion framework for representing and studying SU(2) and SU(3) symmetries, providing new methods for their analysis.

Findings

Constructed Casimir operators for SU(2) and SU(3) using quaternions and octonions.

Demonstrated that quaternion and octonion formalisms effectively handle symmetry generators and properties.

Provided a systematic approach to analyze flavor symmetries in particle physics.

Abstract

An attempt has been made to investigate the global SU(2) and SU(3) unitary flavor symmetries systematically in terms of quaternion and octonion respectively. It is shown that these symmetries are suitably handled with quaternions and octonions in order to obtain their generators, commutation rules and symmetry properties. Accordingly, Casimir operators for SU(2)and SU(3) flavor symmetries are also constructed for the proper testing of these symmetries in terms of quaternions and octonions.