Geometric Origin of Charge Quantization in Elementary Particles: A Curved-Space Hamiltonian Approach with Electromagnetic Coupling

Abstract

The quantization of electric charge is re-examined within a geometric framework that extends the Hamiltonian formalism to curved spacetime with electromagnetic coupling. By employing the covariant Klein–Gordon equation under minimal coupling and curvature interaction, the study reveals that discrete charge values can arise naturally from geometric phase and holonomy constraints rather than being postulated externally.  The analysis demonstrates that the coupling between curvature and electromagnetic flux produces quantized charge spectra governed by integer topological indices. This geometric mechanism also explains the inherent symmetry between positive and negative charges as a manifestation of spacetime duality.  The formalism reduces smoothly to standard quantum field theory in the flat-space limit, ensuring full compatibility with established results. Overall, the findings suggest that spacetime curvature acts as a “natural quantizer,” transforming continuous field variables into discrete charge states and providing a pathway toward unifying electromagnetism with gravitation under a single geometric principle.