Non-Abelian gauge field effects and its relevance to spinning particle dynamics in the technology of spintronics

We describe formally the precession of spin vector about the k-space effective magnetic field in condensed matter system with spin orbital effects as constituting a local transformation of the electron wavefunction which necessarily invokes the SU(2) transformation rule to ensure covariance. We showed a "no-precession" condition as pre-requisite for the spin gauge field to exert its influence on spin particle motion. The effects of the spin gauge field on spin particle motion were shown to be consistent in both classical and quantum pictures, which hence should underpin theoretical explanations for important effects in anomalous Hall, spin Hall, spin torque, optical Magnus, geometric quantum computation.