SU(N) Irreducible Schwinger Bosons

TL;DR

This paper introduces a new method for constructing SU(N) irreducible representations using Schwinger bosons, simplifying their structure and avoiding multiplicity issues, akin to the SU(2) case.

Contribution

The authors develop SU(N) irreducible Schwinger bosons satisfying specific constraints, enabling straightforward construction of all SU(N) representations without multiplicity problems.

Findings

All SU(N) irreducible representations are monomials of (N-1) types of bosons.

Representations are free of multiplicity issues.

Method simplifies the construction of SU(N) representations to the SU(2) case.

Abstract

We construct SU(N) irreducible Schwinger bosons satisfying certain U(N-1) constraints which implement the symmetries of SU(N) Young tableaues. As a result all SU(N) irreducible representations are simple monomials of $(N-1)$ types of SU(N) irreducible Schwinger bosons. Further, we show that these representations are free of multiplicity problems. Thus all SU(N) representations are made as simple as SU(2).