A Zero-Curvature Representation of Electromagnetism and the Conservation of Electric Charge

We show that the laws of electromagnetism in (D + 1)-dimensional Minkowski space-time M, explicitly for D = 1, 2 and 3, can be obtained from an integral representation of the zero-curvature equation in the corresponding loop space L(D-1)(M). The conservation of the electric charge can be seen as the result of a hidden symmetry in this representation of the dynamical equations.

Automated summary

This study demonstrates that the laws of electromagnetism in (D + 1)-dimensional Minkowski space-time M, specifically for D = 1, 2, and 3, can be derived from the integral representation of the zero-curvature equation in the corresponding loop space L(D-1)(M). The conservation of electric charge is attributed to a hidden symmetry in this representation of the dynamical equations.