Journal of Modern Classical Physics & Quantum Neuroscience

Abstract

The quantization of electric charge is traditionally derived from the consistency condition imposed by magnetic monopoles, as originally demonstrated by Dirac [1]. Subsequent developments in the geometric formulation of gauge theory clarified that magnetic flux quantization follows from the integrality of the first Chern class of principal bundles [2-4].

In this work, we present a complementary derivation based on the global structure of the quantum configuration space. Formulating abelian gauge theory in four-dimensional asymptotically flat spacetime as a sum over inequivalent principal bundles classified by H²(M,Z), we show that invariance of Wilson line operators under large gauge transformations [7] constrains electric charges to lie in the lattice dual to the magnetic flux lattice. Electric charge quantization therefore emerges as a global consistency condition of the quantum theory, independently of the existence of dynamical monopole solutions.