Description
In 1998, Alejandro Corichi and Kirill V. Krasnov showed that the loop quantization of sourced U(1) gauge fields leads naturally to the quantization of electric charge. This result arises from the use of holonomy-flux variables, where holonomies (Wilson lines) take values in U(1) and fluxes in R, yielding a phase space locally of the form U(1)xR.
While loop quantization has since been predominantly developed in the SU(2) setting of loop quantum gravity, the U(1) case provides a simpler and instructive arena in which key structural features, such as charge quantization, can be understood.
In this talk, I revisit the loop quantization of electrodynamics and propose an extension based on exponentiated flux variables. This modification leads to a theory with a locally (compact) toroidal phase space, U(1)xU(1). I analyze the resulting form of the Gauss constraint and show how it gives rise to a discrete spectrum of electric charge. These results suggest a broader mechanism for charge quantization rooted in the structure of phase space.