When deriving the conserved currents from continuous symmetries, my book states that we can also add a 4-divergence to the lagrangian density which does not change the action under variation. The four divergence can be transformed into a boundary integral by stokes theorem. However, my book fails to mention any assumptions we are making about this extra term so that it does not contribute to the variation of the action. The final result is the current(adsbygoogle = window.adsbygoogle || []).push({});

J^{μ}=Π^{μ}δΦ-W^{μ}where the W^{μ}is from the four divergence mentioned above ∂_{μ}W^{μ}

My question is: What assumptions, if any, are imposed on the W^{μ}so that it doesn't affect the action under variation so that we can include it in the current?

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# Noetherian currents and the Surface term

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