Hi guys, I'm sure I'm being very stupid here but I'm reading through notes which contain various actions for fields, most of which are very similar, however there is some discrepancies with the way differential operators are shown acting on the fields and I can't for the life of me work out which are equal to which so any advice would be great.(adsbygoogle = window.adsbygoogle || []).push({});

The three forms I can see are, for a real field [itex]\phi[/itex]

[itex]

1) (∂^\mu \phi)(∂_\mu \phi)

[/itex]

[itex]

2) ∂^\mu ∂_\mu |\phi|^2

[/itex]

[itex]

3) \phi (∂^\mu ∂_\mu) \phi

[/itex]

These seem to often be used in very similar places but I can't really see how they relate? This is likely painfully simple and I'm just overthinking it but even just pointing in the right direction would be great, thanks!

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# Equivalence of differential operator terms in action

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