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.

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# Homework Help: 4 vector notation help

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