Not a particularly direct question, just something I don't mathematically understand and would very much appreciate help with.(adsbygoogle = window.adsbygoogle || []).push({});

For some scalar field [itex]\phi[/itex], what would [itex]\partial_{\mu} \phi^{*}\partial^{\mu} \phi[/itex] mean in mathematical terms. ie how would I calculate it?

From what I understand its basically [itex]\Sigma_{\mu}\left(\frac{\partial}{\partial x^{\mu}}\phi \right)^{2}[/itex] because of the complex conjugate in the scalar field, and you sum over repeated indexes.

Also, just to ask, why wouldn't I write this [itex]\partial^{\mu} \phi^{*} \partial^{\mu} \phi[/itex]? Is it because I wouldn't then be allowed to sum over the [itex]\mu[/itex] index?

Or is it something to do with a contraction being Lorentz invariant?

Thanks for any help, let me know if I haven't been clear.

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

Dismiss Notice

Join Physics Forums Today!

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

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

# 4 vector notation help

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