Varying a function

  • #1
Hi i am trying to vary [itex] \int a^{3}(t)(0.5\dot{\phi}^{2}-\frac{1}{2a^2}(\nabla \phi)^{2} -V) d^3 x[/itex]
I understand that one varyies w.r.t phi so it becomes:
[itex] \int a^{3}(t)(\dot{\phi}\delta \dot{\phi}-\frac{1}{a^2}(\nabla \phi)(\delta \nabla \phi) -V'\delta \phi) d^3 x[/itex]

I can't see why it would then becomes [itex] \int (-\frac{d}{dt}(a^{3}\dot{\phi})+a(\nabla^{2} \phi) -a^3V') d^3 x[/itex]

I.e where do the variations go why does it become [itex]\partial_{\mu}[/itex] that then moves before the terms not after them , i realise that the metric used is (-,+++)
 

Answers and Replies

  • #2
mathman
Science Advisor
7,858
446
I don't know the answer, but I think you would do better by putting your question in the calculus forum.
 

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