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Peskin and Schroeder, equation 2.51

  1. Aug 27, 2010 #1
    Hi

    I am struggling to justify

    [tex] D(x-y) \approx e^{-i m t} [/tex] as [tex] t \rightarrow \infty [/tex]

    from

    [tex] \int dE \sqrt{E^2-m^2} e^{-i E t} [/tex].

    I thought I might get some insight from discretizing, as

    [tex] e^{-i m t} \sum_{n=0}^{\infty} \epsilon \sqrt{ n \epsilon ( 2 m + n \epsilon ) } e^{-i n \epsilon t} [/tex]

    but I don't understand how to approximate or take the limit of the sum.

    I also tried to work backwards from

    [tex] G : (E^2-m^2)^{3/2} e^{-i E t} [/tex]

    and replacing extra E's with d/dt's and ended up with a differential equation
    for the result,

    [tex] G = i [ t (d^2/dt^2 + m^2) + 3 d/dt ] D(x-y) [/tex]

    but I am having trouble putting the pieces together to solve it.

    Assistance would be greatly appreciated.
     
    Last edited: Aug 27, 2010
  2. jcsd
  3. Oct 11, 2010 #2
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