ok, I hope this is the right place to post this, that's my first post here! ^_^(adsbygoogle = window.adsbygoogle || []).push({});

Well I'm deriving the Noether's Current in terms of an improved energy momentum tensor and by now all the knowledge about tensors algebra and so on came from my own sadly. I'm stuck with a matter that probably reveals anything that is not really clear about tensors..

I have:

[itex]\frac{\partial}{\partial(\partial_{\mu}\phi)} \partial_{\rho}\phi\partial^{\mu}\phi[/itex]

now I would write:

a) [itex]=\frac{\partial}{\partial(\partial_{\mu}\phi)} (\partial_{\rho}\phi)\eta^{\mu\mu}(\partial_{\mu} \phi )=(\partial_{\rho}\phi)\eta^{\mu\mu}[/itex]

a') [itex]=\frac{\partial}{\partial(\partial_{\mu}\phi)} \delta^{\mu}_{\rho}(\partial_{\mu}\phi)(\partial^{\mu}\phi)=

\delta^{\mu}_{\rho}(\partial^{\mu}\phi)=

\delta^{\mu}_{\rho}\eta^{\mu \mu }(\partial_{\mu} \phi )=

(\partial_{\rho}\phi)\eta^{\mu\mu}[/itex]

and I hope they are correct.. but then I thought.. what about this one??

b) [itex]=\frac{\partial}{\partial(\partial_{\mu}\phi)} \delta^{\mu}_{\rho}(\partial_{\mu}\phi)\eta^{\mu \mu}(\partial_{\mu}\phi)=

2(\partial_{\rho}\phi)\eta^{\mu\mu}[/itex]

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# Tensor gymnastic in Noether's Current

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