- #1

muppet

- 608

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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

[tex](\phi\phi\phi\hat{\phi})^2[/tex]

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.