Iterated dimensional regularization

1. Jun 27, 2011

zetafunction

let be the 2-loop integral

$$\iint d^{k}pd^{k}qF(q,p)$$

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 $$F(p,e^{-1} )$$

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. Jun 27, 2011

ardie

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.

3. Jun 28, 2011

zetafunction

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.