An Explicit and Simple Relationship Between Two Model Spaces

TL;DR

This paper establishes a clear and straightforward relationship between the basis of the $SU(3)$ model space and that of $SU(2) imes SU(2)$ or $SO(1,3)$ using generating functions, providing new insights into their connections.

Contribution

It presents the first explicit correspondence between the basis of $SU(3)$ model space and that of $SU(2) imes SU(2)$ or $SO(1,3)$ through generating functions.

Findings

Explicit relationship between $SU(3)$ and $SU(2) imes SU(2)$/$SO(1,3)$ basis spaces

Use of generating functions to establish the correspondence

Simplifies understanding of the connections between these model spaces

Abstract

An explicit and simple correspondence, between the basis of the model space of $SU(3)$ on one hand and that of $SU(2)\otimes SU(2)$ or $SO(1,3)$ on the other, is exhibited for the first time. This is done by considering the generating functions for the basis vectors of these model spaces.