# Divergent series in perturbation theory of quantum field theory

1. Nov 6, 2005

### eljose

if we know that the divergent series in perturbation theory of quantum field theory goes in the form:

$$\sum_{n=0}^{\infty}a(n)g^{n}\epsilon^{-n}$$ with

$$\epsilon\rightarrow{0}$$

then ..how would we apply the renormalization procedure to eliminate the divergences and obtain finite results?....why can not this be done to NOn-renormalizable series?..thanks.

2. Nov 7, 2005

### Haelfix

Ok first of all you are abusing terminology a little bit.

What you want to do is first and foremost, choose a regularization scheme.

Namely, pick a cutoff on that infinite series. The details of the renormalization process depends crucially on the details of which type of cutoff you pick.

3. Nov 8, 2005

### Kruger

I would not chose this cutoff. Chose something like exp(-epsilon*n)
If esilon-->0 then exp(-epsilon*n)=1.