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!