Advantages of Non-Associative Sedenionic QED Without UV-Divergence and Renormalization: Predictions of Lepton Mass and Magnetic Moment Anomaly

We propose a non-associative reformulation of quantum electrodynamics (QED) based on octonionic and sedenionic hypercomplex algebras, replacing the conventional associative Clifford algebra and Dirac gamma matrices. In this framework, the associator — a quantity that vanishes in standard QED — becomes physically active, inducing Yukawa-type screening and regulating self-energy divergences. This removes the need for renormalization and resolves the vacuum catastrophe. Lepton masses arise algebraically from associator norms without invoking the Higgs mechanism, yielding accurate predictions for the electron, muon, and tau masses. Likewise, anomalous magnetic moments (g-2)/2 for all three charged leptons emerge naturally from generation-dependent associator corrections, matching experimental values to high precision — including the muon anomaly — without perturbative loop corrections. The model introduces gauge fields valued in non-associative algebras and generalizes the field strength tensor to include commutators and associators. This results in a divergence-free, highly predictive quantum field theory with no adjustable parameters. Our results suggest that non-associativity provides a deeper algebraic foundation for quantum dynamics, encoding mass, anomaly, and vacuum structure in a unified formalism.