Covariant - tensor method for quantum groups and applications I: $SU(2)_{q}$

TL;DR

This paper introduces a covariant tensor method for quantum groups, specifically $SU(2)_q$, enabling calculation of q-deformed Clebsch-Gordan coefficients and establishing links with covariant oscillators and tensor operators, with potential extensions to other quantum groups.

Contribution

It presents a novel covariant tensor approach for $SU(2)_q$, facilitating calculations of q-deformed Clebsch-Gordan coefficients and connecting with covariant oscillators, extending the toolkit for quantum group analysis.

Findings

Developed a covariant tensor method for $SU(2)_q$

Calculated q-deformed Clebsch-Gordan coefficients

Linked covariant oscillators with tensor operators

Abstract

A covariant - tensor method for $SU(2)_{q}$ is described. This tensor method is used to calculate q - deformed Clebsch - Gordan coefficients. The connection with covariant oscillators and irreducible tensor operators is established. This approach can be extended to other quantum groups.