SU(N) Coherent States and Irreducible Schwinger Bosons

TL;DR

This paper constructs SU(N) coherent states using irreducible Schwinger bosons, providing a framework analogous to Heisenberg-Weyl coherent states, and characterizes them by eigenvalues of SU(N) Casimir operators.

Contribution

It introduces a novel method for constructing SU(N) coherent states based on irreducible Schwinger bosons, extending the understanding of group representations.

Findings

Coherent states are labeled by eigenvalues of SU(N) Casimir operators.

States are characterized by (N-1) complex orthonormal vectors.

The construction parallels the Heisenberg-Weyl coherent states.

Abstract

We exploit the SU(N) irreducible Schwinger boson to construct SU(N) coherent states. This construction of SU(N) coherent state is analogous to the construction of the simplest Heisenberg-Weyl coherent states. The coherent states belonging to irreducible representations of SU(N) are labeled by the eigenvalues of the $(N-1)$ SU(N) Casimir operators and are characterized by $(N-1)$ complex orthonormal vectors describing the SU(N) group manifold.