Difference in the number of operators between coupled and uncoupled basis for the general SU(n) Lie algebra

TL;DR

This paper investigates how the number of operators needed to specify states in SU(n) Lie algebra varies between coupled and uncoupled bases, especially as the dimension increases, revealing systematic differences.

Contribution

It provides a systematic analysis of the difference in operator counts between coupled and uncoupled bases for SU(n), highlighting how this difference evolves with dimension.

Findings

Number of operators differs systematically between bases as dimension increases

The difference in operator counts changes predictably with higher dimensions

Insights into basis choice implications for high-dimensional Lie algebra representations

Abstract

For the cases of irreducible representation, the complete set of operators necessary to specify uniquely the states. There are two ways of representing the state, using uncoupled and coupled basis. Here we discuss, how the number of operators for the cases of coupled and uncoupled basis changes as well as their difference with the increase of dimension. For higher dimensional groups this number difference changes systematically.