I was reading about the momentum-energy tensor (or stress-energy tensor), at one point the author says,(adsbygoogle = window.adsbygoogle || []).push({});

"

[tex]\theta^{\mu\nu} = (\partial^\mu\phi)(\partial^\nu\phi) - g^{\mu\nu}L[/tex]

This is clearly symmetric in [tex]\mu[/tex] and [tex]\nu[/tex]."

[tex]\theta^{\mu\nu}[/tex]: is the stress-energy tensor

[tex]\phi[/tex] is a scalar field

[tex]g^{\mu\nu}[/tex] is the metric (+---)

L is the lagrangian density

My question (I'm not an expert in tensors) is how do you see that it's "clearly" symmetric? another silly question: when do we need to symmetrize and antisymmetrize tensors?

Please, tell me guys if this isn't the right place for my question.

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# This is clearly symmetric!

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