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Integration question in Peskin and Schroeder

  1. Aug 3, 2012 #1
    Hi all, I'm stuck with proving the last step of (2.51) in Peskin and Schroeder:
    $$\begin{align} D(x-y) &= \frac{1}{4\pi^2}\int^\infty_m dE \sqrt{E^2 - m^2}e^{-iEt}\\
    & \approx_{t \to \infty}\ \ e^{-imt}\end{align}$$

    I've read on another post that the solution is to use the method of stationary phase, but I do not see how this applies, as [itex]E[/itex] is not a rapidly oscillating function...?

    Thoughts appreciated,

    Ianhoolihan
     
  2. jcsd
  3. Aug 4, 2012 #2

    strangerep

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  4. Aug 4, 2012 #3
    Thanks strangerep,

    The thread I referred to was https://www.physicsforums.com/showthread.php?t=424778.

    Your post does make it clearer, in that it stems from a limit of the exact solution (Bessel function). I will look through the details soon.

    Cheers.
     
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