The Momentum-First Dirac Equation: A Unified Hamiltonian for Fermions in Stationary Spacetimes

The Momentum-First (M-First) framework posits that gravity's primary role is to modify the kinematic rules of quantum mechanics. We apply this principle to Dirac fermions in stationary spacetimes, deriving a single, unified quantum Hamiltonian from first principles. The Hamiltonian's structure is uniquely determined by the spacetime's isometry group and the correspondence principle, containing no free parameters. In its static limit, it resolves the neutron star shallow heating puzzle via a gravitationally induced contextual mass. In its rotational limit, it provides the theoretical foundation for the anomalous Earth fly-by velocity shifts. The theory further predicts novel, testable phenomena, including a gravitational spin-Hall effect and a gravitational screening of charge. The ability of a single, coherent framework to solve existing anomalies and predict new physics marks it as a compelling paradigm for quantum-gravity interactions.