The transformations of the electromagnetic potentials under translations

Details The transformations of the electromagnetic potentials under translations The transformations of the electromagnetic potentials under translations

2000-06-05

arxiv.org/abs/hep-th/0006029v2

Physics

High Energy Physics

High Energy Physics - Theory

References to work by Jackiw and others are added

Scientific paper

I consider infinitesimal translations $x'^{\alpha}=x^{\alpha}+\delta x^{\alpha}$ 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 $A'_{\gamma} (x') = A_{\gamma}(x)+\partial_{\gamma} [\delta x_{\beta} A^{\beta}(x)]$, which differs from the usually assumed invariance $A'_{\gamma} (x') = A_{\gamma}(x)$, by the gauge transformation $\partial_{\gamma} [\delta x_{\beta} A^{\beta}(x)]$.

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