# Connection between four current and Noether current.

1. Jan 17, 2012

### thepopasmurf

Hi,
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 $J^{\mu}=-i(\varphi\partial\varphi^{*}-\varphi^{*}\partial\varphi)$ can be cancelled out if one includes the electromagnetic interaction term $-eJ^{\mu}A_{\mu}$ 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,