A zero-curvature representation of electromagnetism and the conservation of electric charge

Abstract

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

References in corpus (2)

• Integrable theories and loop spaces: fundamentals, applications and new developments
• A simple formula for the conserved charges of soliton theories