A query on the (old) motivation for renormalizable theories
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Jul14-11, 04:58 AM
That's awesome - thanks very much. I had a suspicion that was the case but have only ever worked at such a miniscule order I wasn't sure if it was the case. Thanks mate!
An n-point vertex function is a sum of one-particle-irreducible diagrams with external propagators removed. (There is also a nonperturbative definition in terms of Legendre transforms of the functional integral with a source, but I don't remember it precisely enough to quote it.)
For 2-2 scattering, you need the 4-point vertex function. But when you compute it, at high enough orders, you will have sub-diagrams that involve n-point vertices for arbitrarily high n. And these have to be renormalized, so you will need the corresponding parameters.