1. Not finding help here? Sign up for a free 30min 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!

Qft peskin eqn 2.54

  1. Jan 6, 2009 #1
    QFT Peskin p.30 eqn 2.54

    1. The problem statement, all variables and given/known data

    i am perplexed with eqn 2.54 peskins introductory qft. just cant make out how to arrive at it from the previous step. i think that there are dirac delta funtions involved but simply cant make it out. can somebody help? provide some hint? thanks in advance for ur time

    3. The attempt at a solution
    [tex]\int\ \frac{d^3p} {(2\pi)^3}\ \{ \frac {1}{2E_p}\ e^{-ip.(x-y)}\left|_{p^0 = E_p}\ +\ \frac {1}{-2E_p}\ e^{-ip.(x-y)}\left|_{p^0 = -E_p}\ \}= \int\ \frac{d^3p} {(2\pi)^3}\ \int\ \frac{dp^0} {2p^0}\ e^{-ip.(x-y)}\ \{ \delta (p_0-E_p) +\delta (p_0+E_p)\ \}[/tex] [tex]= \int\ \frac{d^3p} {(2\pi)^3}\ \int\ dp^0\ e^{-ip.(x-y)}\ \delta(p^2-m^2)[/tex]

    dont know if iam on the right track.pls correct me if am wrong.
    Last edited: Jan 6, 2009
  2. jcsd
  3. Jan 7, 2009 #2
    It would be good, if you would write down the equation you want to prove, since I dont have the mentioned book...
  4. Jan 7, 2009 #3
    What P&S are doing in Eqn. 2.54 is re-writing a three-dimensional integral as a four-dimensional integral:
    [tex]\int\frac{d^3p}{(2\pi)^3}\frac{1}{2E_p}[\exp(-ip\cdot(x - y)) - \exp(ip\cdot (x - y))] = \int\frac{d^3p}{(2\pi)^3}\int\frac{dp^0}{2\pi i}\ \frac{-1}{p^2 - m^2}\exp(-ip\cdot(x - y)),[/tex]
    where [tex]x^0 > y^0[/tex].

    What I would do to understand this is start from the latter form and perform the [tex]p^0[/tex] integral. Break up the denominator into
    [tex]p^2 - m^2 = (p^0)^2 - \textbf p^2 - m^2,[/tex]
    which has poles at
    [tex]p^0 = \pm \sqrt{\textbf p^2 + m^2} = \pm E_p.[/tex]
    Contour integration should produce the first expression in the original post [which P&S give as an intermediate step] without too much trouble.
  5. Jan 7, 2009 #4
    i jumped into conclusions before reading the text further. sorry. anyways thanks so much for ur time & help.:smile:
    Last edited: Jan 7, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Qft peskin eqn 2.54
  1. Peskin QFT p.21 (Replies: 2)

  2. @ Peskin eqn 2.54 (Replies: 2)