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Iterated dimensional regularization

  1. Jun 27, 2011 #1
    let be the 2-loop integral

    [tex] \iint d^{k}pd^{k}qF(q,p) [/tex]

    where k is the dimension so we regularize it by dimensional regularization

    the my idea is the following

    i integrate oper ''q' considering p is constant to get [tex] F(p,e^{-1} ) [/tex]

    here e is the parameter inside k=4-e

    after dimensional regularization over q i have an integral over 'p' , so i apply dimensional regularization again to obtain a regularized value

    can this be done ?? i mean can we apply dimensional regularization iteratively over each variable ??
  2. jcsd
  3. Jun 27, 2011 #2
    not quiet. if the integral is doable or not will depend on what the function F(q,p) represents. of course to do an integral over n variables you have to perform the integral n times, but you also need n-1 expressions relating your n-variables all together. so if you have a relation that will translate F(q,p) in terms of F(k(p),p), then you can do the integral over dp first taking q to be a constant.
  4. Jun 28, 2011 #3
    but can it be done iteratively ??

    for example i make dimensional regularization over 'p' keeping 'q' constant and afterwards i make use of dimensional regularization over q to get a finite result.
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