Operator-Based Derivation of Coupling Constants and Running QCD from a Unified Mass–Charge Framework

We extend the operator framework  Z = M + iQ to explicitly derive the coupling constants of the fundamental interactions. The real sector, M, produces gravity, while the imaginary sector, Q, generates the gauge interactions: U(1) (electromagnetism), SU(2) (weak), and SU(3) (strong). We calculate all couplings at a chosen reference scale and derive the renormalization-group (RG) flow of the QCD coupling constant directly from the spectral structure of Q. Low-energy limits reproduce known experimental values, with the SU(3) coupling exhibiting running behavior, while the U(1) and SU(2) couplings remain approximately constant at accessible energies. This approach provides a fully operator-based, predictive mechanism linking microscopic operator structure to macroscopic force strengths and the QCD running coupling.