In scalar QED, there are two noether currents ##J_{global}## and ##J_{local}##corresponding to the global and local gauge transformations respectively.(adsbygoogle = window.adsbygoogle || []).push({});

In QED, the two currents are exactly the same. But in scalar QED, they are totally different.

$$J_{global}^\mu=i e (\phi^\dagger \partial^\mu\phi-\phi\partial^\mu\phi^\dagger)$$ and

$$J_{local}^\mu=i e (\phi^\dagger D^\mu\phi-\phi D^\mu\phi^\dagger)$$

where ##D^\mu## is covariant derivative. So my question is how to interpret these two quantities? which one represents the charge of the scalar field?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The interpretation of noether currents in scalar QED

**Physics Forums | Science Articles, Homework Help, Discussion**