Invariants, Projection Operators and $SU(N)\times SU(N)$ Irreducible Schwinger Bosons

TL;DR

This paper develops a framework using SU(N) Schwinger bosons to construct and analyze coupled irreducible representations of SU(N)×SU(N), including projection operators, irreducible bosons, and Clebsch Gordan coefficients.

Contribution

It introduces a novel method to explicitly construct coupled irreducible representations and projection operators for SU(N)×SU(N) using Schwinger bosons and invariants.

Findings

Explicit construction of projection operators in terms of invariant group generators

Development of irreducible Schwinger bosons for coupled states

Calculation of SU(N) Clebsch Gordan coefficients as matrix elements

Abstract

We exploit SU(N) Schwinger bosons to construct and analyze the coupled irreducible representations of $SU(N) \times SU(N)$ in terms of the invariant group. The corresponding projection operators are constructed in terms of the invariant group generators. We also construct $SU(N) \times SU(N)$ irreducible Schwinger bosons which directly create these coupled irreducible states. The SU(N) Clebsch Gordan coefficients are computed as the matrix elements of the projection operators.