1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: QFT question

  1. Nov 16, 2007 #1
    1. The problem statement, all variables and given/known data

    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]


    [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.
  2. jcsd
  3. Nov 16, 2007 #2
    Sigh. Nevermind, there was a typo in my second integral, Eq. (15) is actually

    [itex]Z = \int D \varphi e^{i \int d^4 x [-\frac{1}{2}\varphi(\partial^2+m^2)\varphi + J\varphi]}[/itex] which can be obtained easily by integration by parts on the [itex](\partial \varphi)^2[/itex] term:

    [itex]\int d^4 x\, (\partial \varphi)^2 = -\int d^4x\, \varphi \partial^2\varphi[/itex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook