The Schwinger SU(3) construction. II. Relations between Heisenberg-Weyl and SU(3) coherent states

Abstract

The Schwinger oscillator operator representation of SU(3), studied in a previous paper from the representation theory point of view, is analyzed to discuss the intimate relationships between standard oscillator coherent state systems and systems of SU(3) coherent states. Both SU(3) standard coherent states, based on choice of highest weight vector as fiducial vector, and certain other specific systems of generalized coherent states, are found to be relevant. A complete analysis is presented, covering all the oscillator coherent states without exception, and amounting to SU(3) harmonic analysis of these states.