From UD Theory to QCD: Emergent Color SU(3) and Quark Charges

This paper derives the color SU (3) gauge symmetry and fractional quark charges of quantum chromodynamics entirely from the first-principles UD field equations. The core mechanism originates from the three-dimensional tangent space of the \ (S³\) constraint manifold, which is rigorously derived from the global normalization axiom of UD theory. This geometric structure provides three degenerate directions for the fundamental matter fields \ (DD\) and \ (DU\). We construct three complex matter scalar fields and verify the exact global U (3) invariance of their Lagrangian via algebraic derivation. Spacetime-localized color rotational consistency mathematically necessitates the introduction of compensating vector gluon fields, yielding the full QCD Lagrangian containing eight non-Abelian gauge bosons. The observed quark fractional charges \ (+2/3\) and \ (-1/3\) are uniquely determined as the only rational solution satisfying color degeneracy, proton charge normalization, and the UD mutual containment principle that excludes all pure single-attribute physical states. No external symmetry assumptions or empirical inputs are required. Quark confinement emerges as a direct consequence of the non-Abelian structure of the emergent SU (3) gauge group. Key Results: The \ (S³\) internal geometry naturally generates three degenerate color degrees of freedom The matter sector exhibits exact global U (3) symmetry from first principles Gluon fields are mathematically required for local gauge consistency (not postulated) Up and down quark fractional charges are uniquely fixed by UD axioms Quark confinement is implied by the non-Abelian SU (3) gauge structure