  As one of the most elegant theories in physics, Yang-Mills (YM) theory not
only incorporates Maxwell's equations unifying electromagnetism, but also
underpins the standard model explaining the electroweak and strong interactions
in a succinct way. Whereas the highly nonlinear terms in YM equations involving
the interactions between potentials and fields retard the resolution for them.
In the $U(1)$ case, the solutions of Maxwell's equations are the
electromagnetic waves, which have been applied extensively in the modern
communication networks all over the world. Likewise the operator solutions of
the YM equations under the assumptions of weak-coupling and zero-coupling
predict the $SU(2)$ angular-momentum waves, which is the staple of this work.
Such angular-momentum waves are hopefully realized in the experiments through
the oscillations of spin angular momentum, such as the ``spin Zitterbewegung''
of Dirac's electron.
