Gauge SU(3) connection for the geometrical collective Yang-Mills model

The SU(3) gauge theory of collective modes is a significant extension of the Bohr-Mottelson legacy model in which collective wave functions of the Euler angles and $\beta, \gamma$ become vector-valued in an irreducible representation of SU(3). This SU(3) describes internal vorticity in the rotating frame. A symplectic model reciprocity theorem relates this ``vortex" SU(3) to Elliott SU(3) and the shell model. The differential geometry of Yang-Mills theory introduces a new ingredient, a gauge interaction, which couples the angular and vortex momenta via a covariant derivative and  bundle connection. The new SU(3) gauge model builds on prior work about the Yang-Mills SO(3) gauge group model (J. Phys. A {\bf 48} (2015), EPL {\bf 119} (2017) 62001).