Developments on the Jordan-Schwinger construction and contraction for the $su_q(2)$

TL;DR

This paper explores the q-deformed Jordan-Schwinger construction and contraction for su_q(2), revealing new non-linear expressions that connect the q-boson algebra with the original algebra, extending previous theoretical understanding.

Contribution

It introduces new non-linear expressions that facilitate the contraction process in the q-deformed Jordan-Schwinger construction, enhancing the theoretical framework.

Findings

New non-linear expression for contraction

Extended analysis of q-deformed algebra relations

Clarification of contraction process in q-deformed case

Abstract

The contraction and Jordan-Schwinger construction connect the $su(2)$ and the heisenberg algebra, going in oposite directions. This persists in the q-deformed cases, but in a slightly different way. This work investigates this further, discussing some details and results found in the litterature and presenting some new ones, including a non-linear expression that leads the contraction back to the original q-boson algebra used in the Jordan-Schwinger construction.