Onamor
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Not a particularly direct question, just something I don't mathematically understand and would very much appreciate help with.
For some scalar field \phi, what would \partial_{\mu} \phi^{*}\partial^{\mu} \phi mean in mathematical terms. ie how would I calculate it?
From what I understand its basically \Sigma_{\mu}\left(\frac{\partial}{\partial x^{\mu}}\phi \right)^{2} 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 \partial^{\mu} \phi^{*} \partial^{\mu} \phi? Is it because I wouldn't then be allowed to sum over the \mu 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.
For some scalar field \phi, what would \partial_{\mu} \phi^{*}\partial^{\mu} \phi mean in mathematical terms. ie how would I calculate it?
From what I understand its basically \Sigma_{\mu}\left(\frac{\partial}{\partial x^{\mu}}\phi \right)^{2} 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 \partial^{\mu} \phi^{*} \partial^{\mu} \phi? Is it because I wouldn't then be allowed to sum over the \mu 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.