- #1
pleasehelpmeno
- 154
- 0
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 realize that the metric used is (-,+++)
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 realize that the metric used is (-,+++)