What Causes Divergences in QFT?

[eljose]

more than a proper topic this is a question...my question is if all the divergences that appear in QFT are due to integrals in the form:

$$\int_{0}^{\infty}dkk^{m}$$

with m=-1 (logarithmic),0,1,2,3,4,5,...

if not i think that for any other divergences you could express them as:

$$\int_{0}^{\infty}dkF(k)= \sum_{r=0}^{\infty}a(r)\int_{0}^{\infty}dkk^{r}$$

r=0,1,2,3,4,5,... and a(r) the coefficients of the series expansion for the function F(k) of course K here is the "momentum" modulus $$p=\hbar{k}$$

 

[DarMM]

Roughly speaking yes, all integrals are of this form. Though there is the issue of overlapping divergences and subgraphs, e.g. a single loop integral might result in a logarithmically divergent term that contains the integration variable of another loop integral.