The applications of the general and reduced Yangian algebras

TL;DR

This paper explores the applications of general and reduced Yangian algebras Y(sl(2)) and Y(su(3)), demonstrating how reduced forms can disentangle initial states and influence decay channels in quantum systems.

Contribution

It introduces a special constraint that simplifies Yangian representations into block-diagonal forms and compares their effects on quantum states and decay processes.

Findings

Reduced Yangian algebras can disentangle initial states.

General Yangians cannot disentangle initial states.

Y(su(3)) generators affect decay channels.

Abstract

The applications of the general and reduced Yangian Y(sl(2)) and Y(su(3)) algebras are discussed. By taking a special constraint, the representation of Y(sl(2)) and Y(su(3)) can be divided into two 2 \times 2 and three 3 \times 3 blocks diagonal respectively. The general and reduced Yangian Y(sl(2)) and Y(su(3)) are applied to the bi-qubit system and the mixed light pseudoscalar meson state, respectively. We can find that the general ones are not able to make the initial states disentangled by acting on the initial states, however the reduced ones are able to make the initial state disentangled. In addition, we show the effects of Y(su(3)) generators on the the decay channel.