Coupling Multiple SU(2) Groups Into A SU(3) Group Structure

Abstract

A specific algebraic coupling model involving multiple quantization axes is presented in which previously indistinguishable SU(2) symmetry groups become distinguishable when coupled into a SU(3) group structure. The model reveals new intrinsic angular momentum (or isospin) eigenvectors whose structural symmetries are detailed, some of which are not available for groups having only one quantization axis available for configurations. Additionally, an intrinsic cyclic ordering of the quantization axes and internal geometric phase relations between the basis states naturally fall out from the algebraic properties of the group. The nature of the coupling into a SU(3) symmetry group also allows for the definition of both positive and negative basis states along each quantization axis relative to the center of the group. These basis states configurations mimic those observed in color-charge and electroweak theories.