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Perturbation theory.

  1. Feb 2, 2008 #1
    Hi, i am stuck at this problem , let be the divergent quantity

    [tex] m= clog(\epsilon) +a_{0}+a_{1}g\epsilon ^{-1}+a_{2}g\epsilon ^{-2} +a_{3}g\epsilon ^{-3}+.........+ [/tex]

    where epsilon tends to 0 and g is just some coupling constant and c ,a_n are real numbers.

    then i use the Borel transform of the function [tex] F(t)= \sum_{n=0}^{\infty}a_{n} \frac{t^{n}}{n!} [/tex] in this case

    [tex] m= clog(\epsilon)+ \int_{0}^{\infty}dtF(t/\epsilon)e^{-t} [/tex]

    my question is, does this last expression have only 2 divergent quantities ? , mainly the one due to log(e) and the second involving the poles of [tex] F(t/\epsilon) [/tex]
  2. jcsd
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