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I was wondering if someone could explain how the Noether current and four-current are connected.

For context, I'm going through a derivation to show that local phase symmetry requires the electromagnetic field. I'm at a stage where the I have a Noether current of a complex field (for Klein-Gordon Lagrangian), the next bit of the derivation then says that the Noether current [itex]J^{\mu}=-i(\varphi\partial\varphi^{*}-\varphi^{*}\partial\varphi)[/itex] can be cancelled out if one includes the electromagnetic interaction term [itex]-eJ^{\mu}A_{\mu}[/itex] and then does a gauge transformation.

How are the two J terms related, because it seems to say that the four-current is equal to the Noether current.

Thanks,

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# Connection between four current and Noether current.

Can you offer guidance or do you also need help?

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