Ladder operators approach to representation classification problem for Jordan-Schwinger image of su(2) algebra

TL;DR

This paper introduces a ladder operator method to classify states in the Jordan-Schwinger image of su(2) algebra, constructing a canonical basis and defining commuting operators for irreducible representations.

Contribution

It presents a novel ladder operator approach for classifying representations of the Jordan-Schwinger image of su(2), including basis construction and operator definition.

Findings

Constructed a canonical basis for irreducible representations.

Defined self-adjoint operators for complete commuting sets.

Provided a classification scheme for the Jordan-Schwinger image of su(2).

Abstract

The eigenvalues of the complete commuting set of self-adjoint operators determine the classification of states. We construct a classification for the image of the Jordan-Schwinger mapping of the su(2) algebra. We use the ladder operator approach to construct a canonical basis of irreducible representations and define the self-adjoint operators of the complete commuting set.