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A Delta function in continuation back to Minkowski space

  1. Nov 23, 2016 #1
    The Green's function for a scalar field in Euclidean space is

    $$(2\pi)^4\delta^4(p+k) \frac{1}{p^2+m^2}$$

    however when I continue to Minkowski space via GMin(pMin)=GE(-i(pMin)) there's seems to be a sign error:

    $$(2\pi)^4\delta^4(-i (p+k)) \frac{1}{-p^2+m^2}=(2\pi)^4\delta^4(p+k) \frac{i}{-p^2+m^2}=-(2\pi)^4\delta^4(p+k) \frac{i}{p^2-m^2}$$

    where I used δ(-ix)=(1/(-i))δ(x).

    The error seems to be that the scaling of the delta function should instead be δ(-ix)=δ(ix)=(1/(i))δ(x).

    But how do we know this? For real 'a' it can be argued δ(ax)=(1/|a|)δ(x) on the grounds that δ is postive, but δ(-ix) is not positive as it's not even a real number.
     
  2. jcsd
  3. Nov 28, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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