I've been trying to get a rough understanding of what renormalization involves (in a particle physics context; I'm aware it has many other applications eg. condensed matter) but it hasn't quite clicked yet. The things I have in my head so far are as follows:(adsbygoogle = window.adsbygoogle || []).push({});

- A particle will be surrounded by a cloud of virtual particles, which affect the measurement of the particle's properties, ie. if you collide two electrons, the energy of the collision determines how deep into this cloud you penetrate, and thus the charge of the electron you measure is not actually a constant, but rather depends on your experiment. So it is said that the electron has some intrinsic 'bare' charge, but this is not what is being measured.

- In Feynman diagrams, you have your basic "tree-level" diagrams, but also you can have additional diagrams that contain virtual particle loops.

- If you want to calculate an amplitude for, say, a scattering process, you need to take these additional loop diagrams into account.

- The energies/momenta of the incoming/outgoing final state particles do not determine what the energy/momenta of a virtual particle must be, so instead one must integrate over all energies/momenta to determine the contribution that some loop diagram makes to the overall scattering amplitude.

- However, sometimes these integrals blow up to infinity (and I think it's that for high momentum this is called an "ultraviolet divergence", conversely an "infrared divergence" is an infinity corresponding to momentum becoming very small?). So, these infinite contributions ruin your amplitude calculation.

==> Solution required, "renormalization".

- First of all, instead of integrating all the way to infinite momentum, one imposes some cut-off upper limit to the integral, then your orginal integral can be split into a finite part and a divergent part. The imposition of a cut-off is referred to as "regularization".

*** (I'm aware of there being different ways to do this regularization - it may not be a momentum cut-off that is used, but rather other things such as a dimension cut-off that are more useful/appropriate [for reasons like preserving gauge invariance I think?] but they sound like more complicated things and I'm trying to understand in the simplest way possible. And regardless of the specific details of the cut-off, they should always produce only one result). ***

Anyway, assuming nothing I've said so far is incorrect, here's where I start getting shaky.

At this point the material I've read starts talking about of some "counter-terms" (are these also called "radiative corrections?") that get added to the Lagrangian to cancel out the divergent parts of these integrals, and the bare parameters (charges, couplings, fields) in the Lagrangian get redefined... somehow... by some sort of subtraction? And somewhere in there, you require an experimentally measured value made at one specific collision energy? (or rather, one measurement per parameter involved?) And it is said that your theory is "renormalizable" if this can be done with a finite number of counter-terms? The infinities get absorbed into the bare parameters? (which is fine, there's supposedly nothing wrong with them being infinite?) And you end up with a Lagrangian in terms of "renormalized" parameters, with no dependence on the arbitrary, user-selected cut-off/"regularization".

But I don't fully understand what I just said there. What I'm hoping for here is if someone can talk about what I'm getting at in that previous paragraph. Also I'm not sure if perturbation theory / power series expansions have any relevance to the scattering example I've mentioned here, but I have seen them in some of the texts I've looked at, just not quite sure if / how they fit into this picture.

Thanks.

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# A Understanding renormalization / regularization basics

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