A class of generalised Jordan-Schwinger maps

TL;DR

This paper introduces a new class of generalized Jordan-Schwinger maps that realize the generalized sl(2) algebra through two independent Generalized Heisenberg Algebras, extending the standard algebraic structures with potential physical interpretations.

Contribution

It presents a compact, simple generalization of the Jordan-Schwinger map that includes the standard case and connects to composite particles with angular momentum.

Findings

Generalized JS map includes standard JS map as a special case

Realizes generalized sl(2) algebra via two GHA

Suggests physical interpretation in terms of composite particles

Abstract

In this article we introduce a class of generalisations of the Jordan-Schwinger (JS) map which realises the recent proposed generalised sl(2) (G-sl(2)) algebra via two independent Generalised Heisenberg Algebras (GHA). Although the GHA and the G-sl(2) algebra exhibit more general algebraic structures than the Heisenberg and sl(2) algebras, the generalised JS map presents a compact and simple structure wich includes the standard JS map as a particular case. Finally, since in the GHA there is a physical interpretation in terms of composite particles, we will carry out this assertion in a manner that the generalised sl(2) algebra could be related to composite particles with angular momentum.