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Derivative of d'Alambert operator?

  1. Nov 11, 2014 #1
    Hi guys,

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

    Thanks!
     
  2. jcsd
  3. Nov 12, 2014 #2

    ShayanJ

    User Avatar
    Gold Member

    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 [itex] \partial_\nu \Box \phi=\partial_\nu (\partial^\mu \partial_\mu \phi) [/itex]. I don't see a reason that makes it zero identically!
     
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