Natural Science Forum / Physics / Research / February 2005

Renormalization is a phenomenon of perturbative methods. Its already
present in perturbation theory in normal quantum theory, because the
calculated perturbed wave-function doesn't automatically have norm 1.

René.

I'm not sure how far you are in P&S, but in
ch7 there's a section called "Field Strength
Renormalization" that derives some properties
of 2-point functions using non-perturbative
methods. One thing they show is how a single
particle state can evolve through an infinity
of multiparticle intermediate states, leading
to infinite "Z" terms corresponding to the
usual ones that arise in 1-loop QED. That
might partially answer your question.

Yes. Renormalization is needed since the continuum limit of a QFT is
well-defined only if the coupling constants are taken to be a suitable
function of the cutoff.

See my theoretical physics FAQ at
        http://www.mat.univie.ac.at/~neum/physics-faq.txt

Perturbation methods are used only because no one knows how to do
4D QFT without it. But in 2D and 3D one knowns how to do QFT
nonperturbatively, and there one can see that renormalization
is independent of perturbation theory.

Arnold Neumaier