From UD Theory to Particle Physics: A Unified Derivation of the Structure of Matter

This paper derives the gauge structure of particle physics 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. In the vector realization, the four components form an SU(2) doublet, naturally yielding the gauge structure of the electroweak unification theory. Introducing color indices, the natural symmetry group for three color indices is SU(3), corresponding to the strong interaction. Fermions emerge naturally as excitations of DU , and the Dirac equation is obtained as a generalization from quantum mechanics. This demonstrates that the gauge structure of the Standard Model of particle physics is not an independent fundamental theory, but a natural manifestation of the primordial theory in the vector realization.