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Estimating size of loop integrals

  1. Jun 22, 2010 #1
    Is there a way to measure how large a numerical value a loop integral will give?

    For example, take this integral over loop momenta k:

    [tex]\frac{1}{k^2+m^2} \frac{1}{(k+p)^2+m^2} [/tex]

    How does it compare to setting p=0:

    [tex]\frac{1}{k^2+m^2} \frac{1}{(k)^2+m^2} [/tex]

    or to a double integral over loop momenta k and q:

    [tex]\frac{1}{k^2+m^2} \frac{1}{q^2+m^2}\frac{1}{(k+q)^2+m^2} [/tex]

    All I know how to do is to Wick rotate, regulate, renormalize, and I also know that [tex]\frac{1}{k^2+m^2}[/tex] should really be: [tex]\frac{1}{k^2+m^2-i\epsilon}[/tex] so that the integral over the energy component will not blow up - any blow up will be in the 3-momentum component.

    But I'm not sure what's really going on with all these integrals. Some of them are infinite and you have to renormalize, and you're left with a finite part, but how to estimate the magnitude of the finite part?
  2. jcsd
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