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Fourier Transform quartic interaction

  1. Nov 30, 2009 #1
    Hi all,

    This might be simple but I haven't figured out a way to do this.

    Basically I have the result in coordinate space and 3+1 spacedimensions, to order lambda^2,

    \frac{(-i \lambda)^2}{2!} \int dx dy (i D_F(x-y))^2 (i D_F(x1-x)) (i D_F(x2-x)) (i D_F(x3-y)) (i D_F(x4-x))

    which is just a bubble with 4 legs, 2 on each side. But now I want to put it into momentum space using Fourier transforms. Maybe I am getting lost in the details but I know that one of the legs transforms as,

    i D_F(x1-x) ---> \int \frac{d^4p}{(2\pi)^4} \exp^{-i p * (x1-x)} \frac{i}{p^2-m^2+i\epsilon}

    I also know that some delta functions will come out to knock out some of the integrals, but I can't figure it all out. Does someone know how to do this and can show me explicitly?

    Thanks much,
    Brett
     
  2. jcsd
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