Talk:Renormalization group

Rewrite

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

This article is so poorly written one wonders if the contributors even understand what they are talking about. Junk it and start from scratch.....

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)

I removed a line about the number of microscopic interactions being of order 10^{-23}. Presumably, the editor who wrote this was thinking about atoms in a box. However, RG flow is relevant in many physical contexts; in most relativistic quantum field theories for example and this statement is not accurate there. I also added a line explaining why we see only particles of spin 0, 1/2 and 1 at low energies. cheers, Perusnarpk (talk) 21:40, 30 July 2008 (UTC)

User:R.e.b. re-inserted the statement about there being 10^{-23} microscopic interactions. This is incorrect, hence I've removed the statement again. Please do not re-insert without justifying it here. Second, I've elaborated the explanation of why we see only particles of spin less than 1 at low energies. The idea I am trying to express is that the standard model is an effective field theory, just like other quantum field theories. Since, the interactions of particles with spin larger than 1 are necessarily irrelevant, we do not see these particles in a low energy effective theory. In a `theory of everything' like string theory, these particles are indeed predicted at high energies, of order, the string scale, but they decouple at observable energies. If my explanation is not clear, please refine or discuss here. 202.159.224.74 (talk) 08:42, 10 August 2008 (UTC)

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.

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)

Too technical

Unfortunately, this article does a poor job of explaining RG in a context independent of any particular application. Notably missing from it is any mention of RG in Chaos/Complexity theory, where it is critically important in Feigenbaum's proof of universality for a class of functions giving rise to chaos under a period doubling route. The article also reads -- as do many Wikipedia articles on technical topics -- like it is intended for specialists (though I wouldn't know why they would want to read it), as it contains impenetrable references to a raft of other things that were defined elsewhere. Article authors need to recognize that non-specialists turn to Wikipedia for definitions, and that the articles like this are of poor quality unless they are intelligible to someone not immersed in the field. —Preceding unsigned comment added by 98.228.35.247 (talk) 20:21, 21 November 2010 (UTC)

Amen. David Spector (talk) 02:54, 4 March 2011 (UTC)

Group?

I have a question. The article speaks about the "renormalization group", but nowhere does the article prove that there is a structure that forms a group. Is the renormalization group a group, or is it just another bad name in Physics? I study Physics. But the mathematical definitions tend to be a lot better, in the sense that they mean what one expects them to mean. In this case, I feel there is something I am not getting, because I don´t see what the group is and if it is useful to think of transformations in this way. So, is there a group hidden there, or is better to ignore the name and just read the article? --190.188.2.122 (talk) 01:16, 17 February 2011 (UTC)

I am not sure, but I think that the group is the group of scale transformations — making the small things larger with corresponding changes in the charges, masses, and coupling constants. It has an identity element — leaving all the distances, time durations, charges, masses, and constants the same. An inverse transformation would just reverse all the changes. The group operation is composition of two transformations to give the composite transformation, e.g. doubling distances and trebling distances combine to form multiplying distances by six. Does anyone know if this is correct? JRSpriggs (talk) 06:25, 17 February 2011 (UTC)

The article makes the point that "there need not be an inverse for a given RG transformation. Thus, the renormalization group is in fact a semigroup." I think JRSpriggs is exactly right that the "group" in "renormalization group" refers to the set of scale transformations, except for the fact that they don't have inverses (the same low energy/long distance physics can result from many different underlying high energy/small distance theories) so renormalization group is really a (slight) misnomer. Mattysb (talk) 13:54, 21 February 2011 (UTC)

To Mattysb: Thank you for clarifying that. JRSpriggs (talk) 02:58, 22 February 2011 (UTC)

Regarding group properties: Shankar (http://arxiv.org/abs/cond-mat/9307009) has a short discussion on this issue. As far as I know the RG is a semigroup since the inverse element does not necessarily exist - this was stated earlier in this discussion. —Preceding unsigned comment added by 155.69.182.225 (talk) 13:21, 22 March 2011 (UTC)

Throughout the article, "RG" is used ambiguously, albeit in comportance with established and immutable physics practice. "RG", in fact, refers to both "renormalization structure", the Wilsonian vision of mutation across scales; and also the "renormalization group trajectory", a bona fide group, indeed a Flow (mathematics), with an identity and an inverse, for renormalizable theories — admittedly a small subset of theories, but nevertheless the ones studied first, best, and with the most standard results taught first. In this latter case, a system such as QED may be evolved forward and backwards, and the variation of its coupling monitored and compared. I would recommend leaving things as they are, but still making perfunctory efforts to implicitly contrast the group with a unique RG trajectory, to the grand multidimensional flows of the Wilsonian scheme. Cuzkatzimhut (talk) 21:06, 27 March 2011 (UTC)

Physical Predictions

It would be nice if the anonymous 178.197.254.3 editor discussed the object of his persistent edits reverted by JRSpriggs, soundly, in my opinion. Gell-Mann and Low, in the reference cited, went beyond formal solution of the finite renormalization group equation to an expression equivalent to the rise of the QED coupling with energy precisely as quoted in the LEP measurement. Beyond mainstream professional opinion, Prof Harald Fritzsch stakes his professional opinion on it, in print (would 178.197.254.3 require the specific citation? DOI:10.1142/S0217751X10049864). Do S & P do so in the papers quoted, in such specificity? Do B & S? Is the paternity of this type fo prediction contested? Please discuss, before tendentious repetitive repartee edits! Cuzkatzimhut (talk) 20:35, 1 May 2011 (UTC)