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arXiv · 2203.15682

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

G. Luchini·V. B. Zaché
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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.

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G. Luchini, V. B. Zaché. 2022-03-29. A zero-curvature representation of electromagnetism and the conservation of electric charge. https://doi.org/10.1007/s13538-022-01131-6

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