The Standard Form of Special Potential Relativity: A Unified Framework for Extended Quantum Field Theory and General Relativity

This paper introduces a comprehensive theoretical framework that extends the fundamental equations of quantum mechanics and general relativity. We present the LLS Equation, a generalization of the Dirac equation incorporating additional matrix structures governed by an extended Clifford algebra, derived from first principles starting from a modified mass-energy relation. The LLS Mass-Energy Relation modifies the conventional E = mc2 formula to include potential-dependent corrections. From these foundations, we rigorously derive corresponding extensions to quantum electrodynamics (LLS-QED), quantum chromodynamics (LLS-QCD), and the equations of general relativity (LLS-GR). The theoretical consistency is established through detailed analysis of gauge invariance, renormalizability, and symmetry properties. We provide explicit one- and two-loop calculations demonstrating renormalizability. Phenomenological implications are explored across hadronic physics, neutron star structure, and cosmology, showing potential to address outstanding problems such as the proton radius puzzle and the muon g −2 anomaly. Systematic parameter determination using Bayesian inference shows decisive statistical evidence favoring the LLS framework over standard theories, with ∆AIC = −121.2 across multiple datasets.