Using Dimensional Regularization to Tame Divergent Momentum Integrals

[kassem84]

Dear all,
Dimensional regularization is a very important technique to remove the divergence from momentum integrals.
Suppose that you have to calculate a quantity composed of three integrals over k_1, k_2 and k_3 (each one is three dimensional). the integral over k_3 gives ultra violet divergence. Whereas, the remained integrals give finite numbers.
I have some questions:
1) Can we play with these integrals (performing change of variables or calculating one or two of these integrals) before performing dimensional regularization?
2) Can we transform these 3 integrals into one dimensional integrals that is divergent and then do the dimensional regularization?

Thanks in advance.
Best regards.

 

[Simon_Tyler]

If you are only doing a one-loop calculation then you can be really slack and do all those things you mentioned. If you are doing a multiloop calculation and using minimal subtraction then you have to be more careful and have everything dimensionally regularized (with the same dimension parameter) throughout the whole calculation, only taking the d->4 limit at the end.
Of course, the only difference should be in finite counterterms that can be fixed using well defined renormalization scheme.

 

[kassem84]

Thanks very much, it is a useful note.