Renormalisation group transformation- Peskin

[muppet]

Hi all,

I'm trying to understand Peskin's treatment of the Wilsonian approach to renormalisation, in chapter 12. The essential (i.e textbook-independent) question I have is: why does integrating out the high-momentum modes generate all possible interactions?

I understand part of the answer- one has a coupling of high-and low frequency modes, and doing the path integral over the high frequency modes (denoted by a circumflex) means that terms like
$$(\phi\phi\phi\hat{\phi})^2$$
will generate a phi^6 interaction.

What I think it is that I don't understand is the role played by the momentum of the external particles. Peskin argues that "a more exact treatment would taylor expand in [the external momenta of the diagrams]", but it isn't clear to me what's being expanded (a diagram? the n-point correlation function?) or why we have to expand in this Wilsonian treatment when we wouldn't ordinarily. To be honest, some complementary references would be good.

Thanks in advance.

 

[atyy]

I'm not sure this is close enough, but something similar happens in Wilsonian renormalization applied to statistical physics.

http://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2008/lecture-notes/
The big picture is given in L7, III.E, p44.
The details as to how the additional terms are generated are given in L11, IV.F p64, 65.

I imagine a translation to HEP is something like that on p22 of http://arxiv.org/abs/hep-lat/9807028