The Reduced properties and applications of the Yangian algebras

TL;DR

This paper explores the simplified properties of Yangian algebras Y(sl(2)) and Y(su(3)), demonstrating their applications in quantum systems and particle states, leading to disentangled final states.

Contribution

It introduces a special constraint that reduces the representation of Y(su(3)) into block-diagonal form and applies these reduced algebras to quantum and particle physics problems.

Findings

Reduced Y(su(3)) representation into 3x3 blocks

Application to bi-qubit systems yields disentangled states

Application to meson states achieves disentanglement after transformation

Abstract

The reduced properties and applications of Yangian Y(sl(2)) and Y(su(3)) algebras are discussed. By taking a special constraint, the representation of Y(su(3)) can be divided into three 3 * 3 blocks diagonal based on Gell-mann matrices. The reduced Yangian Y(sl(2)) and Y(su(3)) are applied to the bi-qubit system and the mixed light pseudoscalar meson state respectively, and are both able to make the final states disentangled after acting on the initial state by the transition operator, composed of the generators of Yangian.