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Klein-Gordon propagator

  1. Feb 7, 2008 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations
    Show that the KG propagator
    [tex] G_F (x) = \int \frac{d^4p}{(2\pi)^4} e^{-ip.x} \frac{1}{p^2-m^2+i\epsilon} [/tex]
    satsify
    [tex](\square + m^2) G_F (x) = -\delta(x) [/tex]

    3. The attempt at a solution
    I get
    [tex](\square + m^2) G_F (x) = - \int \frac{d^4p}{(2\pi)^4} (p^2-m^2) e^{-ip.x} \frac{1}{p^2-m^2+i\epsilon} [/tex]
    but where do I go from there?
     
    Last edited: Feb 7, 2008
  2. jcsd
  3. Feb 7, 2008 #2

    pam

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    Cancel the numerate and denominator p^2-m^2.
    The i epsilon is just a direction how to take the contour, and is negligible here.
    The remaining integral is \delta^4.
     
  4. Feb 7, 2008 #3

    malawi_glenn

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    Science Advisor
    Homework Helper

    how does (p^2-m^2)/(p^2-m^+i*epsilon) cancel?

    I would try to do the limit of epsilon -> 0+
     
    Last edited: Feb 7, 2008
  5. Feb 8, 2008 #4

    pam

    User Avatar

    That's what
    "The i epsilon is just a direction how to take the contour, and is negligible here."
    means.
     
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