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Gaussian Integral with Denominator in QFT

  1. Apr 2, 2015 #1
    Hi all, so I've come across the following Gaussian integral in QFT...but it has a denominator and I am completely stuck!

    [tex] \int_{0}^{\infty} \frac{dx}{(x+i \epsilon)^{a}}e^{-B(x-A)^{2}} [/tex]

    where a is a power I need to leave arbitrary for now, but hope to take between 0 and 1, and [itex] \epsilon [/itex] is arbitrarily small.

    Does any one have any suggestions on how to tackle this? If not, I'd like to leave a arbitrary, but perhaps is can be set to 1/2. Would this then be doable? Thanks for any help!!
  2. jcsd
  3. Apr 3, 2015 #2


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    ## \int_0^\infty \frac{e^{-B(x-A)^2}}{(x+i\epsilon)^a} \, dx## could be rewritten as ## \int_{i \epsilon} ^\infty \frac{e^{-B(z-A-i\epsilon)^2}}{(z)^a} \, dz##
    I am thinking some sort of complex integration technique might help.
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