- #1

Ameno

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This might be a stupid question, so I hope you are patient with me. When I look for the definition of the energy-momentum tensor in terms of the Lagrangian density, I find two different (?) definitions:

[tex]{T^\mu}_\nu = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\partial_\nu \phi - {\delta^\mu}_\nu \mathcal{L}[/tex]

[tex]{T^\mu}_\nu = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\partial_\nu \phi - {g^\mu}_\nu \mathcal{L}[/tex]

Which of the two is correct? Is this somehow a matter of convention or something like that? I have seen both more than once.