How Does Dimensional Regularisation Lead to a Finite Perturbation Expansion?

[latentcorpse]

I am trying question 3 in this paper:
http://www.maths.cam.ac.uk/postgrad/mathiii/pastpapers/2006/Paper49.pdf

I am on the bit "Describe in outline how the functional integral with dimensional
regularisation leads to a finite perturbation expansion for the four dimensional quantum
field theory in terms of the action..."

Now I was just going to describe how we can use dimensional regularisation to identify the poles arising from loop integrals we come across when working out greens functions and from that we can deduce what the necessary counter terms are for use in renormalisation. after we add the counter terms and work everything out the the bare lagrangian $\mathcal{L}_\text{B}=\mathcal{L}+\mathcal{L}_{\text{counter}}$ all divergences are removed and the integral is rendered finite.

However, it is talking about functional integrals and the integrals we have in regularsation/renormalisation are normal integrals. what do you reckon i have to do?

 

[BigJDubs]

In order to answer this question, you will need to familiarize yourself with the concept of a functional integral. A functional integral is a type of integral that can be used to compute the expectation value of a quantum field theory. The idea is that, instead of performing a regular integral over all possible states of the fields, one instead performs an integral over all possible field configurations. This allows us to capture the effects of the interactions between different fields in the theory. Once we have a functional integral for a given theory, we can use dimensional regularisation to identify the poles arising from loop integrals. This allows us to determine the necessary counter terms that are required to renormalise the theory. By adding these counter terms to the bare Lagrangian, we can remove all divergences and render the integral finite. This then gives us the perturbation expansion for the four-dimensional quantum field theory.