Quantum ChromoElectroDynamics (QCED): Unification of Strong and Electroweak Interactions via U(1, 3) × U(1, 3)

This paper presents Quantum ChromoElectroDynamics (QCED), a unified theory that interprets the weak interaction as a mixed relativistic effect of the strong (color) interaction and the electromagnetic interaction, analogous to the magnetic field as a relativistic effect of the electric field and the nuclear force as a residual effect of the color interaction. By introducing the non-compact unitary group U(1, 3)×U(1, 3) as the fundamental structure unifying spacetime and internal symmetries, we prove that this group naturally contains the Lorentz group SO(1, 3),the color group SU(3)c, and two U(1) factors. Its symmetry breaking simultaneously generates massless gluons and photons, as well as massive W ± and Z bosons.On this basis, we derive the weak mixing angle θW satisfying the concise relation sin2θW (MU ) = 1/(1 + 4π2) as a high-energy boundary condition. Through renormalization group evolution, this relation is in excellent agreement with the experimental value sin2θW (MZ) = 0.23122(4), revealing the geometric origin of electromagnetic and weak interactions. Furthermore, we systematically establish a unified differential and integral equation framework for the Gell-Mann matrices,the CKM matrix, and the PMNS matrix. we rigorously prove that the CKM and PMNS matrices must be real orthogonal direction cosine matrices, with all matrix elements being real, thus containing no CP-violating phases. Consequently, CP violation must originate from other mechanisms, such as the geometric difference between the quark and lepton mixing matrices. We derive the three fundamental laws of the CKM and PMNS matrices (determinant and trace, orthonormality, cross product and cofactor relations).