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Mathematics
05-03-2009, 11:11 PM
The Euler-Lagrange equation for a field reads:

\partial_\alpha \left( \frac{\partial \mathcal{L}}{\partial (\partial_\alpha G_{\mu \nu} )} \right) - \frac{\partial \mathcal{L}}{\partial G_{\mu \nu}} = 0.

Where G_{\mu \nu} is the metric tensor.

Anyone know if there's an alternative formulation of the equation, something like:

\frac{\partial \mathcal{L}}{\partial G_{\mu \nu} } = 0,

but not exactly that. I remember my supervisor writing it up on the board but I can't seem to find it anywhere on the net. Anyone know what I'm trying to find or what i'm on about?