The Comparison between the Infinitesimal Operators for SU(3) and Boson Operators in Cartan-Weyl Basis

TL;DR

This paper compares the infinitesimal operators and boson operators for SU(3) and SL(3,c) in the Cartan-Weyl basis, providing detailed calculations relevant for particle physics models.

Contribution

It offers a detailed comparison and explicit calculations of operators for SU(3) and SL(3,c) in the Cartan-Weyl basis, highlighting their similarities and differences.

Findings

Explicit forms of infinitesimal operators for SU(3) and SL(3,c)

Comparison reveals concise representations in SL(3,c)

Useful for theoretical models in particle physics

Abstract

We present the detailed calculation of the infinitesimal operators and the boson operators for SU (3) in Cartan-Weyl basis. They have been used extensively as theoretical models for particle physics. We make a comparison between them, alongside with SL(3,c), which displays the concise appearance.