Talk:Renormalization group

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At last I was able to rewrite completely the article. Of course, it is only a draft and needs lots of improvements. I'm preparing myself some more pictures. Sorry I forgot to sign and add summary of changes! Javirl 14:20, 2 November 2005 (UTC)

I find this article lacks a guide. Sometimes it goes into too much technical detail in math and sometimes leaves things too vague. I think this article should be split into parts. In the first one the very idea should be explained, mostly Kadanoff blocking with pics. The second one should be for RGT, fixed points, relevant-irrelev.-marginal operators, the semigroup character and universality classes. As a third one, although historically it might have come first, I'd add renormalized perturbation theory: Callan-Symanzik and applications to particle physics. Then, links to more specific techniques: Real Space RG (BRG, DMRG...), Momentum Space RG (diagrammatic, exact RG), RPT... and finally a section on the history of RG techniques. As addenda, other topics may be mentioned: relation to fractals, conformal field theory, etc. If nobody is opposed, I'll put my hands to this in a few days. Javirl 16:24, 20 September 2005 (UTC)

What is an "infrared attractor"? Not found via google.... NealMcB 00:30, 2004 Jan 22 (UTC)

No, I've never heard these terms either. Nor can Google find "infrared repellor". However, the term infrared fixed point does appear many times. See http://www.lns.cornell.edu/spr/1999-08/msg0017563.html for a reference. Also, ultraviolet fixed point. -- The Anome 07:54, 14 May 2004 (UTC)

I doubt that the characterization of 'attractor' and 'repellor' are correct. You get a continuum limit if you have an ultraviolet fixed point. The critical point of a statistical field theory corresponds to an infrared fixed point. Each phase is controlled by an attractive fixed point in it, which is usually an infrared fixed point and corresponds to homogeneity and trivial correlations. Critical points are always unstable in at least one direction.

The article is atrocious in its present state. I'll come in for a cleanup soon. — Miguel 14:34, 2004 May 25 (UTC)

I have redirected renormalization to this page. This was the content of the renormalization stub article:

A method of removing singularities from certain calculations in quantum mechanics. See also Renormalization group.

— Miguel 07:27, 2004 May 28 (UTC)

Hmmm... seems like there really should be a separate article on renormalization itself, maybe focusing more on techniques in diagrammatic QFT. It seems odd that the article attributes the notion of renormalization to Gell-Mann and Low; they were more associated with the renormalization group, right? Renormalization goes back at least to Schwinger, Feynman and Tomonaga, though they may not have fully realized what they were dealing with prior to the renormalization group concept. --Matt McIrvin 03:06, 3 Oct 2004 (UTC)

I seem to recall that there are also a couple of Russians who wrote on the renormalization group before Gell-Mann and Low, but were not credited in the West until much, much later. I can't remember the names of the Russian physicists, nor have I been able to track down this bit of trivia. If I had to guess I'd say that Bogoliubov must have been one of them, but I might be wrong. — Miguel 08:15, 2004 Oct 4 (UTC)

It was Bogoliubov and Shirkov. I'll see if I can find the reference. -- CYD

Shirkov gives the references in his overview, which I added as a reference. He also mentions Petermann and Stückelmann as the first to bring in the whole group idea. -- sebastianlutz

The link to the beta function wrongly points to the mathematical Euler beta function. This is NOT what is called the beta function in RG. There the beta function describes the change of the coupling constant(s) with the scale parameter. -- CBL

[edit] Relevant and irrelevant operators, universality classes

From this section it follows that for example temperature, pressure and volume are relevant observables. Translating back to the RG behaviour the magnitude of these observables is supposed to increase as the observed scale is increased. I don't see what that is supposed to mean. Perhaps someone could elaborate on this? --MarSch 12:27, 4 May 2006 (UTC)

[edit] Perturbation expansion

This statement, that I suspect is incorrect,is from the Momentum Space RG section

Momentum-space RG is usually performed on a perturbation expansion (i.e., approximation). The validity of such an expansion is predicated upon the true physics of our system being close to that of a free field system.

Please confirm that this indeed wrong or please elaborate on the details if it happens to be true. As far as I understand, the validity of any perturbation rests on the convergence properties of the perturbative series.

[edit] Elements of RG theory

Shouldn't RG rather be a monoid, since a 1-element exists and semigroup is (not always, but often — and as well @wikipedia) defined without 1-element? --CHamul 10:24, 14 November 2006 (UTC)