On the Geometric Dynamics of Electromagnetic Fields --- From Abelian to Non-Abelian

Electromagnetic fields have been considered to belong only to Abelian systems, yet this may only be part of the physical truth. This paper reveals that electromagnetic fields possess intrinsic non-Abelian properties. Based on Maxwell’s equations and combined with differential geometric, this study conducts the covariant properties of divergence and curl under curvature conditions, and identifies the fundamental mechanism underlying the intrinsic non-Abelian characteristics, namely the bidirectional coupling mechanism between field strength and curvature. On this basis, we obtain exactly three steady-state curvature solutions: the zero-curvature solution corresponds to Abelian photons and electromagnetic waves, while the non-zero solutions correspond to non-Abelian electromagnetic particles. This framework naturally yields the electron mass and Planck constant. And, numerous physical phenomena can be self-consistently explained, including the physical origin of elementary charge, the reason behind the existence yet unobservability of magnetic monopoles, the geometric origin of the proton-electron mass ratio, etc.