- #1
noospace
- 75
- 0
Homework Statement
I'm studying from Zee's QFT in a nutshell. On page 21, I don't understand how he uses integration by parts to get from Eq (14) to Eq (15), ie from
[itex]Z = \int D \varphi e^{i \int d^4 x \{ \frac{1}{2}[(\partial \varphi)^2 - m^2 \varphi^2] + J\varphi \}}[/itex]
to
[itex]Z = \int D \varphi e^{i \int d^4 x [-\frac{1}{2}(\partial^2+m^2)\varphi + J\varphi]}[/itex].
Is he suggesting that [itex]\int d^4x \varphi^2 = \int d^4x \varphi[/itex] and [itex]\int d^4x (\partial\varphi)^2 = \int d^4x( -\partial^2 \varphi)[/itex]? If so, I'm failing to see why this should be the case.