- #1

Xezlec

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**same**sign.

Two pages later, it considers a scalar field [itex]\phi(x^0,\mathbf{x})[/itex] with a Lagrangian density [itex]\mathcal{L}=\mathcal{L}(\phi,\partial_\mu\phi)[/itex], and concludes that [itex]\frac{\partial\mathcal{L}}{\partial\phi}-\partial_\mu(\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)})=0[/itex]. Now, unless I am having some massive brain fart on how covariant and contravariant work, the time-varying and space-varying terms have

**opposite**signs. Right?

What gives? Why are the signs different between these two situations?