  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.
