If you have a Lagrangian of the form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]L=\phi \partial^2 \phi[/tex]

how would you derive its equation of motion? All the books seem to say to treat this Lagrangian as if it were only a function of the field, and not derivatives of the field.

So to calculate this they seem to do a product rule:

[tex]\partial^2 \phi+\phi \partial^2=0[/tex]

The latter term is somehow equal to the first term, so you get:

[tex]2\partial^2 \phi=0[/tex]

Is this generally true, that if you have some scalar operator D sandwiched between two fields:

[tex] L=\phi D \phi [/tex]

then the EOM is:

[tex]2 D \phi=0 [/tex] ?

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# Question about Lagrangian

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