Derivative of d'Alambert operator?

[Dixanadu]

Hi guys,

So I've ended up in a situation where I have $\partial_{\mu}\Box\phi$. where the box is defined as $\partial^{\mu}\partial_{\mu}.$ I'm just wondering, is this 0 by any chance...?

Thanks!

 

[ShayanJ]

You shouldn't use same greek letters. Because the d'Alembertian of a scalar field is a scalar and when you differentiate that, you'll get a vector. So you should write $\partial_\nu \Box \phi=\partial_\nu (\partial^\mu \partial_\mu \phi)$. I don't see a reason that makes it zero identically!