From UD Theory to Electromagnetism: A Unified Derivation of Gauge Fields

This paper derives electromagnetism as a natural consequence of the vector realization from a single fundamental axiom. The axiom is based on the universe originating from the critical state U = D, and through the logical necessity of “mutual containment”, the four-aspect structure UU , UD, DD, DU is derived. Generalizing the scalar field U to a four-vector field U µ , and starting from the total normalization axiom and the principle of least action, the vector field action is established. Variation with respect to Uν directly yields the Maxwell equations ∂µF µν = j ν . In the static limit, it reduces to Coulomb’s law, and the transverse modes correspond to massless photons. This demonstrates that electromagnetism is not an independent fundamental theory, but a natural manifestation of the primordial theory in the vector realization.