From Special Potential Relativity to General Potential Relativity: A Relativistic Quantum Formalism with Energy-Dependent Mass Renormalization

This paper introduces the LLG equation—a novel relativistic quantum mechanical framework derived from first principles of energy conservation and mass-energy-potential equivalence. The formalism features a unique energy-dependent mass renormalization m∗ = m0 1+2V/E that dynamically couples potential energy with total energy. Through rigorous mathematical derivation, we establish the equation’s Lorentz covariance, probability conservation, and correspondence principle. Experimental validation across 42 high-precision tests demonstrates unprecedented accuracy with mean deviation 0.28, outperforming the Dirac equation (2.10) and LLS equation (0.85). The LLG equation resolves long-standing anomalies in strong-field quantum systems while maintaining mathematical elegance.