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The transformations of the electromagnetic potentials under translations

Bernd A. Berg
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Abstract

I consider infinitesimal translations $x'^α=x^α+δx^α$ and demand that Noether's approach gives a symmetric electromagnetic energy-momentum tensor as it is required for gravitational sources. This argument determines the transformations of the electromagnetic potentials under infinitesimal translations to be $A'_γ (x') = A_γ(x)+\partial_γ [δx_β A^β(x)]$, which differs from the usually assumed invariance $A'_γ (x') = A_γ(x)$, by the gauge transformation $\partial_γ [δx_β A^β(x)]$.

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Bernd A. Berg. 2000-06-13. The transformations of the electromagnetic potentials under translations. https://arxiv.org/abs/hep-th/0006029

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