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 dy namically 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 strong-field quantum systems demonstrates unprecedented accuracy, outperforming both the Dirac equation and LLS equation. The LLG equation resolves long-standing anomalies in strong-field quantum systems while maintaining mathematical elegance.