This is probably a minor point, but I have seen in some QFT texts the Euler-Lagrange equation for a scalar field,(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \partial_{\mu} \left(\frac{\delta \cal{L}}{\delta (\partial_{\mu}\phi)}\right) - \frac{\delta \cal L}{\delta \phi }=0 [/tex]

i.e. [itex] \cal L [/itex] is treated like a functional (seen from the [itex] \delta [/itex] symbol). But why would it be a functional? Functonals map functions into numbers, and in our case [itex] \cal L [/itex] is a function of the fields (and their derivatives).

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# Lagrangian density for fields

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