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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 oscillation of spin angular momentum, such as the “spin Zitterbewegung” of Dirac’s electron.