Spin Vector Potential as an Exact Solution of the Yang-Mills Equations

The spin vector potential, a gauge field generated by the intrinsic spin of a particle, has recently been proposed as a central element of spin Aharonov-Bohm effect. While its physical consequences have been explored, a fundamental and theoretical question remains: can it be systematically derived from a first-principle gauge theory? In this work, we prove that the spin vector potential $\vec{\mathcal{A}}= k (\vec{r} \times \vec{S})/{r^2}$, together with the Coulomb-type scalar potential $φ=κ/{r}$, emerges as a new family of exact solutions to the non-Abelian Yang-Mills equations in vacuum. This solution, ${\vec{\mathcal{A}}, φ}$, describes a spin-dependent interaction that naturally reduces to the standard Coulomb interaction when spin effects are neglected. Moreover, we demonstrate that the Schr{" o}dinger and Dirac equations incorporating this spin-dependent Coulomb interaction can be solved exactly. Our work not only provides a rigorous gauge-theoretical foundation for the previously proposed spin vector potential, but also establishes a direct link between spin physics and the Yang-Mills gauge theory. This opens new perspectives for understanding spin-dependent interactions, designing spin-dependent quantum phases, and exploring spin-mediated forces in quantum physics.

💡 Research Summary

The paper proposes that a “spin vector potential”—a gauge field proportional to the intrinsic spin of a particle—can be derived as an exact vacuum solution of the non‑Abelian Yang‑Mills (YM) equations. The authors define a vector potential
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