# Talk:Renormalization

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Renormalization was one of the Natural sciences good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
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Current status: Delisted good article

This page should actually explain renormalization (as, say, in QED) rather than redirecting to "renormalization group".

Done! --Matt McIrvin 22:29, 9 Oct 2004 (UTC)

Some more math and pictures now. I don't think I want to get into the details of regularization techniques and such, as more on loop calculation methods would probably obscure the central ideas rather than illuminating them (there may even be too many equations already, but I wanted to at least sketch the outlines of an example). So I'm probably done with major additions, and I think it's getting pretty encyclopedic. --Matt McIrvin 03:49, 17 Oct 2004 (UTC)

Listed as a featured article candidate, but not doing very well for now. People are posting excellent constructive criticisms of the article over there, though, and any help with addressing them is appreciated. I think it's written on a slightly more popular level than most Wikipedia articles on quantum field theory, but it has a long way to go; the most mathematical parts maybe need to be moved somewhere else. --Matt McIrvin 20:01, 17 Oct 2004 (UTC)

## Speculative alternative to handle infinity

Need a little more clarification for laymen: is renormalization the only way to deal with infinity? Theoretically, if in the future human can tap in the unit of space - Planck length/Planck area/Planck volume - then all forces including can be measured down to literally each point in space? Is Planck volume significant? Can... Planck spacetime (to be the unit of spacetime rather than just space) be defined?Mastertek (talk) 14:32, 23 October 2011 (UTC)

## incomprehensible intro

surely for the scientific american level crowd, a better intro can be provided, eg what the heck is a continuum ? etc etcCinnamon colbert (talk) 20:04, 15 September 2008 (UTC)

Hi I had a try at a simpler introduction (I hope) -> User:Lcorman/Draft_Renormalization_Intro Could you give me some feedback on it ? Thanks ! Lcorman (talk) —Preceding undated comment added 12:59, 17 April 2011 (UTC).

## Failed FAC nomination

Self-nom. This is a subject about which much more could be written, but perhaps not within the scope of a single encyclopedia article. Though the material is fairly arcane, I've tried to strike a balance between concreteness and clarification for nonspecialists. - Matt McIrvin 15:12, 17 Oct 2004 (UTC)

• Object IMHO, a featured article should be easily understandable by someone who knows a little about a subject, but who has some (but not a lot) of willingness to learn. I hope this article can be rewritten to achieve this. (After all, Albert Einstein's General Theory of Relativity was a popular book explaining a complicated technical idea to laymen willing to put a small amount of work into it.)
More specifically, but not exhaustively:
In the lead section: what are 'field effects'?; The article states 'Renormalization arose in quantum electrodynamics as a means of making sense of the infinite results of various calculations and extracting finite answers to properly posed physical questions.' What infinite results, what calculations, what sort of physical questions?
Can't understand the diagrams.
Prehistory: What are point particles? What's a back reaction? What is a particle's field? Can 'inertial mass' be explained here - there are links to 'inertia' and 'mass' but not 'inertial mass'. What's a singularity? Did the 'Attempts to deal with the back-reaction' predict bizarre behaviour that was not observed, or not explain bizarre behaviour that was observed?
Divergences in quantum electrodynamics: What are 'divergent integrals'? What is the importance of 'calculations involving Feynman diagrams'?
A loop divergence: There's no way a layman can understand this! Einstein was kind with his maths (from memory, I think he put much of the details of Lagrangians in appendices a casual reader didn't have to look at. Perhaps it would be better to describe the effect of the formulae here and provide a link to a technical page for those interested (and capable of understanding it).
I'm lost by now, so I've given up reading the article. Personally, I think articles that deal with complex scientific ideas for the layman are as important as they are difficult to write. I hope it is possible to rewrite it so anyone can understand it, but until that happens, I vote object to it being a featured article. jguk 18:08, 17 Oct 2004 (UTC)
Fair enough; part of the problem is that we need comprehensible articles explaining all of the rest of physics that provides background for this; I'm afraid that doing it in the renormalization article would turn it into a complete tutorial on calculus, quantum mechanics, particle physics, and classical and quantum field theory. Maybe we're simply not ready to turn something at this level of specialization into a featured article. --Matt McIrvin 18:51, 17 Oct 2004 (UTC)
No so. For example if you start by explaining what field effects are particularly what a field is in the context of QED (QED being a subset of quantum physics - and quantum physics being readily explainable on a rudimentary level. This can be made to be a very interesting article if it is worked on compassionately and with a view of educating someone with a non science degree background. Do not be discouraged and do not discount the added dimension of understanding provided to yourself when you are forced to explain such complexity to a novice. It is a rewarding challenge! prometheus1
I don't think it's impossible to have a featured article out of this subject. I'm sure I've seen elsewhere pages for laymen, with links to more comprehensive pages for those more scientifically minded. Many pages in the non-scientific world, eg cricket are written for everyone, but have lots of links to more specific areas that only cricket-lovers are going to read. I can't see why a scientific subject can't do the same. jguk 19:43, 17 Oct 2004 (UTC)
Weak oppose for now. Too complex. One thing that might help is if the diags were better labelled: at the moment they are very cryptic. When the text is dense, one tends to skip towards the piccies, in which case they need to be fairly self contained. OTOH the stuff about scale-dependence of forces I found very good, thats the closest I've ever come to understanding it -- William M. Connolley 19:32, 17 Oct 2004 (UTC).
• Support with better explanation of diagrams. Are they Feynman diagrams? Label them as such if so. siroχo 05:12, Oct 19, 2004 (UTC)
• Neutral, I want to remind people that the objection that laymen will not understand it only because the subject is too complex is invalid, because it is not an objection that can be dealt with. Andries 16:36, 21 Oct 2004 (UTC)
• It can be dealt with. See Einstein's General Theory of Relativity and Hawking's A Brief History of Time for two examples of making a complex subject understandable for a layman. jguk 19:09, 21 Oct 2004 (UTC)
• That is incorrect. Just because an objection is difficult to deal with, does not make it invalid. It is certainly possible to do to some extent. - Taxman 19:24, Oct 21, 2004 (UTC)
• On second thought, I think you are right that the article can be made more accessible to lay men. Andries 10:05, 24 Oct 2004 (UTC)
• Object. The article is certainly better than most tries I've seen so far too explain the subject, but it is too high level and implicitely assumes quite some familiarity of the reader with physics, especially terminology. I'd judge it higher undergraduate physics level. While it is fine to get into detail, for the benefit of specialists, one should cover the key point before in a language accesible to the layman. Material for this is present, but there is quite some work to be done. Simon A. 21:05, 22 Oct 2004 (UTC)

I'd just like to say that Matt McIrvin did a terrific job with this article. It's the best non-technical (or at least semi-technical) explanation of renormalization I've read, though, like some of the posters above, I'm dubious about whether it's ultimately possible to make this subject completely understandable for laymen (whatever "understanding" means...) Great attempt though!

The only quibble I have is that the article doesn't mention Hans Bethe's classic "back-of-the-envelope" calculation of the Lamb shift. This was the paper that first showed how the infinities in a perturbation expansion can be dealt with, by dumping the divergent terms into a "dressed electron mass". Even though Bethe's method was primitive and incomplete, and doesn't click with modern methods (i.e. Feynman diagrams), it cuts right to the idea of what renormalization means. -- CYD

An anonymous user(86.130.62.19) added a link to an odd webpage. At a glance it appears to be just some understandably motivated bemoaning on the mathematically unrigorous nature of renormalization, propounding the virtue of fixing this problem. For the most part it is an excellent reference from POV skeptical of renormalization's valid(A POV which I share). Unfortunately, it happens to have a buried suggestion that Feynman, et al. were nothing more than frauds. Specifically I dispute its factual accuracy when it says about the award:

• 1965. Feynman, Schwinger and Tomanoga, "for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles".I am not sure what the agricultural reference is about but all they were really proving was that if you subtract infinity from infinity, you can get any answer you want. Check out this recent paper by the Russian scientist V.P. Neznamov. By choosing a different renormalization method, he gets different answers for the Lamb shift and anomalous magnetic moment from Feynman, et al. He seems to be unhappy about this, but in my humble opinion, his unhappiness should not be with specific results, but rather with the fact that with some tweaking, he could get any other answer as well, including, if he really wants it, the "correct" ones.

This statement is very misleading to those who might read that page uncritically. I don't know how renormalization is done but I find this accusation highly improbable. However, this isn't the only guy making this charge of impropriety as a quick googling of "dippy process" reveals. Ideally, the article should talk about these accusations. I for one would like to understand how these people are confused on this matter. --Intangir 03:43, 31 December 2005 (UTC)

The link to cargo cult science, if meant to say that Feynman is not a fraud, only suppports the cause of the website, as it can be seen that Feynman himself was highly unsatisfied with renormalization as can be seen from a quote in that page and from a few others in other pages over the internet. In fact, the "dippy process" was a phrase from one of 'his' speeches! 59.163.146.5 09:47, 20 February 2006 (UTC)

Sorry, "anonymous user" is me (Chris Oakley), the author of the web page. I am certainly not trying to say that Feynman was a fraud, in fact my criticisms of renormalization do not really go much further than those by Feynman himself, and certainly no further than those by Dirac. Besides my web site, I have discussed the validity of the process at length on sci.physics.research, and my thesis throughout is that the results of the renormalization process are shaped by the required form of the result (must be Lorentz invariant, must be gauge invariant, etc.) since one can get any answer one wants when subtracting infinity from infinity. This makes it unaxiomatic. Most HEP theorists seem untroubled by this, but I think the view that the glass is half empty rather than being half full needs to be expressed somewhere. 86.130.62.19 01:03, 27 March 2006 (UTC)

Following on from the above, I might add that I do not subscribe to the we-are-so-smart-that-we-are-allowed-to-break-the-rules-of-mathematics attitude of most HEP theorists. They claim that renormalization is a limiting process, but this is simply untrue. Take, for example, dimensional regularization: a quantity defined only for natural numbers cannot be extended into the real numbers and still less the complex domain. This is obvious, but I struggle to get the devotees of dim. reg. to admit it. The only reason why results are or at least can be independent of the renormalization scheme is because they have decided in advance what the required answer should look like. I do not hear apologies for this mess anything like as often as I feel I should. Chris Oakley 14:50 27 March 2006 (UTC)

I share Chris Oakley's concerns but I tend to feel that the problem is more in the frequent descriptions of renormalized QFT's as beautiful, fundamental or complete, which deceptively suggests that they are consistent with the normative paradigm of mathematical physics. Insofar as they are just recipes, what's the problem? Zargulon 14:14, 27 March 2006 (UTC)

The problem is that the "half full" view that you have just expressed has guided the majority of research in theoretical particle physics research in the last 30 years. "Knock, and it shall be opened unto you," as it says in the bible, but if no-one is knocking, then how can the door be opened? Whilst I am not denying that there are still a handful of people (mainly in Switzerland and Germany) seriously looking at ways of turning the renormalization recipe into a theory, most researchers, including some of the brightest, have been engaged in the Superstring wild goose chase, where replication of the standard model, renormalization included, is their best ambition. Although these people have a lot to say about the need for elegance and beauty in theoretical physics, they do not seem to be overly concerned at the lack of beauty or elegance in this particular context. Chris Oakley 16:45 27 March 2006 (UTC)

I mostly agree with you but don't be too hard on all phenomenologists; some of them spend their working lives subjecting these "recipes" to the very closest scrutiny in the light of experimental data, and we must hope they unearth any inconsistency that exists. It is definitely unsatisfactory that whenever a renormalized qft appears not to work someone decides there are a bunch of new (usually unobservable) mass scales/symmetries/dimensions which just happen to intervene to save their sorry behind. Heck, no-one's even seen the Higgs yet and the universal belief in it has got to be unhealthy. I definitely disagree with you that the brightest people are to be found working on superstrings. Zargulon 17:44, 27 March 2006 (UTC)

Re: your last sentence: they *think* that they are the brightest, and they were often the ones who got the top marks in their undergraduate year, but I share your doubts. A scientist should not be so soft-headed as to work on something just because it is fashionable. He/she should also be concerned about contact with reality. As for inconsistency, this is less of an issue for recipes than theories. One can happily paper over the cracks in recipes in a way that is simply not possible for theories. Or one can introduce spurious concepts with easy "get out" clauses if the idea does not work (e.g. supersymmetry). Chris Oakley 18:10 27 March 2006 (UTC)

The so-called "dubious" web link to my website has now been removed in favour of quotes by Dirac and Feynman sceptical of renormalization. Chris Oakley 07:30, 14 October 2006 (UTC)

## feigenbaum constant

Renormalization apparently figures into chaos theory and the calculation of the Feigenbaum logistic constants (see Feigenbaum constant). Can anyone explain more?Phr 12:29, 14 February 2006 (UTC)

Maybe you mean scaling, not renormalization? Scaling occurs when a statistical mechanics system (e.g. melting ice/freezing water) is near a phase transition. At the critical point, the physics occurs at all length scales at once, and thus require a language very similar to that of the renormalization group. I suppose a system that is at the transition between period-doubling and chaos might also have this kind of ambiguous-scale type effect. See critical exponents, critical opalescence, although the article on phase transitions explains it best. linas 04:10, 17 May 2006 (UTC)
Of course it appears in "the calculation of the Feigenbaum constant". And it's a complete renorm theory not just a scaling . In fact, mathematically renormalization is an operator on a functional (Banach) space that usually serves a purpose of explaining some universality -- pretty much anything can and has been renormalized in dynamical systems: unimodal maps, circle maps, area-preserving maps, flows, Henon maps, etc. As it stands the article describes only QFT RG theory and may be should be called so.

## Zeta function regularization

I removed the section below, after discussion with User:Xerxes314. It appears to contain a number of inaccuracies. The section was initially added by User:Karl-H and cleaned up by Xerxes and myself before we realized there were, ahem, problems. The biggest problem is the absurd claim that non-renormalizable theories can be made renormalizable, which is insane, because non-renormalizable theories have an infinite number of infinities. The minor problem is that the whole idea is awkwardly presented. linas 04:04, 17 May 2006 (UTC)

i think this is a ORIGINAL RESEARCH so the 'zeta regularization ' part should be deleted, it seems jose garcia made all this and it has beeen never published in a well-defined and respectable journal of physics , the only reference is PRESPACE TIME journal reliable?,what do we do i can not see refernces from, except in https://www.encyclopediaofmath.org/index.php/Zeta-function_method_for_regularization

Zeta regularization and renormalization

Julian Schwinger discovered a relationship between zeta function regularization and renormalization, using the asymptotic relation:

${\displaystyle I(n,\Lambda )=\int _{0}^{\Lambda }dp\,p^{n}\sim 1+2^{n}+3^{n}+...+\Lambda ^{n}=\zeta (-n)}$

as the regulator ${\displaystyle \Lambda \rightarrow \infty }$. Based on this, he considered using the values of ${\displaystyle \zeta (-n)}$ to get finite results. Although he reached inconsistent results, an improved formula by Hartle, J. Garcia and E. Elizalde includes

${\displaystyle I(n,\Lambda )={\frac {n}{2}}I(n-1,\Lambda )+\zeta (-n)-\sum _{r=1}^{\infty }{\frac {B_{2r}}{(2n)!}}a_{n,r}(n-2r+1)I(n-2r,\Lambda )}$,

where the B's are the Bernoulli numbers and

${\displaystyle a_{n,r}={\frac {\Gamma (n+1)}{\Gamma (n-2r+2)}}}$.

This reduces every ultraviolet divergence to the case ${\displaystyle n=0.}$ With this procedure one may turn a non-renormalizable theory into a renormalizable one with only two divergent parameters A and B that are the cases of the divergent integrals with ${\displaystyle n=0,-1.}$ For infrared divergences, one may just put ${\displaystyle p=1/q}$ as a change of variable. Other approaches are based on Ramanujan resummation, which is another summability method to give meaning to divergent series and integrals.

Simply stated, this means that, no matter how many different types of divergent ultraviolet or infrared integrals ${\displaystyle I(n,\Lambda )}$ one has, they all can be expressed as a linear combination of ${\displaystyle \zeta (-1),\zeta (-3),\zeta (-5),\ldots }$ and ${\displaystyle I(0)\,}$ (for the case of ${\displaystyle n=-2,-4,-6,-8,\ldots }$, the zeta function is zero; these are the so-called "trivial roots" of the zeta function). Eventually one has only two free parameters left (including the logarithmic divergence) to renormalize in the theory, making it accessible for calculation.

• See the paper http://demoprints.eprints.org/5120/ the authors use the Euler sum formula to reduce every divergent integral to the cases I(0) I(-1) of ${\displaystyle \int _{0}^{\Lambda }dpp^{m}}$ m=0,-1 so you have only 2 divergent parameters left... i would like to hear other people,s argument before the User Linas erase it, i think we should take into account all the arguments. --Karl-H 09:07, 17 May 2006 (UTC)
Regardless of whether the results are correct, it is a violation of Wikipedia policy to post original research. Are you claiming that this is a standard textbook technique for renormalization? -- Xerxes 17:15, 17 May 2006 (UTC)
It,s an anecdotic conclusion, similar to the one posted in the link to Alain Connes, are you trying to say i,m a hoaxer?..check the paper and the google to search: Manuel Angel Valle or www.ehu.es as i did, unless you and your wiki-riends think i,m M. Valle, the same conclusions or similar were found in the book by E. Elizalde Zeta regularization techniques and renormalization i,m a French physicist student, i have nothing to do with the paper, check Elizalde Book or other resources before deleting an article..i hope you don,t consider it a personal attack.--Karl-H 17:50, 17 May 2006 (UTC)
I removed the section because it seemed to be rather shaky, and is based on a rather shakier preprint. The whole thing sounds like a garbled account of dimensional regularization, which is a legitimate technique that has been in use for at least 30 years. Renormalization is a big topic in QFT, and there have been thousands, if not tens of thousands, of papers written on it; some by the finest in physics. Its seemed inappropriate to highlight a rather fractured account of an unpublished paper making a rather unusual claim. I'd prefer that this article stick to widely accepted, widely acknowledged results in the theory of renormalization. linas 04:42, 19 May 2006 (UTC)
Although you have cited the title incorrectly, I looked up this book (Emilio Elizalde's Zeta regularization techniques and applications) and and discovered the following:
Dimensional regularization in curved spacetimes has been termed as ambiguous. The value given by zeta-function regularization coincides, up to a multiple of the normalization parameter, with the one given by dimensional regularization when the extra dimensions are flat.
So zeta regularization seems solid (tho the authors seemed pretty defensive about how most physics authors dismissed their work). I still can't make heads nor tails of what was written in the Wikipedia article tho. Regularization does not "make nonrenormalizable theories renormalizable", no matter how fancy your technique is or how well it works in curved spacetime. Perhaps study of the original zeta-regularization article will be helpful. -- Xerxes 18:19, 19 May 2006 (UTC)
The italicized comments about curved space-time would make an interesting addition to one of these articles; I certianly didn't know that. As to defensiveness: when presented with math, there is a cultural element in theoretical physics that is passed for prof to student, which can be summarized as follows: "Big whoop-dee-doo. Show me something I didn't already know, something worth my time." I remember my student impressions of "Annals of Mathematical Physics" (or whatever it was called): every paper seemed to take 20 excrutiating pages to state a theorem that, for me, was some trite factoid, some a small step in the much longer calculations I had to do to get from here to there. I've since, of course, mended my opinions, and am now enmired in the "trite" math. And so it would be with zeta-function regularization: for a physicist, it's some small step in some long calculation, so of course the typical physicists' reaction might be "golly, you actually found enough to say about it to write a whole book?" :-) linas 04:52, 20 May 2006 (UTC)
OK, let's see if we can reach some consensus. Clearly zeta-function regularization is a fine regularization scheme. In fact, there's already a Wikipedia article on it. The link posted in this article is clearly not of a quality acceptable for Wiki and additionally violates the no-original-resarch policy. As for the text of this section, I think it should be deleted or at least moved to the regularization article. Agree? -- Xerxes 18:02, 21 May 2006 (UTC)
• The question with Zeta regularization is according to Karl-H user could you always put every infrared, UV or logarithmic divergence (using Taylor or other expansions) in the form:

${\displaystyle \int _{0}^{\Lambda }dpp^{m}}$ m integer.

Questionable citation In the further reading on this topic, there is a link to # Introduction to renormalization using zeta regularization http://arxiv.org/pdf/math.GM/0402259

This link does not exist any more because Arxiv has pulled the paper due to "fraudulently claimed institutional affiliation and status." See http://arxiv.org/abs/math/0402259

66.152.232.29 18:12, 7 April 2007 (UTC) Susama Agarwala

## GA Promotion

I have recently reviewed this article & found that it meets the criterion for being a good article. So I have promoted it to GA status. My congratulations to all the contributors for doing a fine job.

Cheers

Srikeit(talk ¦ ) 14:56, 27 May 2006 (UTC)

## GA Re-Review and In-line citations

Members of the Wikipedia:WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. Currently this article does not include in-line citations. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project. Agne 00:12, 26 September 2006 (UTC)

As the section "Attitudes and interpretation" is partly about opinions, we can do some sourcing there. BTW, can anybody explain the relevance of that Chris Oakley's opinion?
Pjacobi 06:18, 26 September 2006 (UTC)
I came across Chris Oakley's ideas before, as he often comments on Peter Woit's blog. I believe he has a PhD in theoretical physics from ~20 years ago, but his ideas about renormalization are far from canonical. I suppose part of the point of an "attitudes and intepretation" might be to include such viewpoints, but I think his work is not really notable enough to include (it's not published in a peer-review journal---in fact rejected outright if I remember correctly). --Jpod2 08:57, 26 September 2006 (UTC)
Fair enough, insofar as Chris Oakley's opinions are just Chris Oakley's. However, they are not. They are also Feynman's, among many others. These criticisms of renormalization, and of how renormalization should be described, have a long and distinguished pedigree, and the discussion they have generated has provided revealing insights in its own right. A paragraph about them on this article would surely be appropriate. Zargulon 10:43, 26 September 2006 (UTC)
Dear Zargulon, I think either you have misunderstood me, or your comment is something of a Straw man. I didn't suggest removing Feynman's comments. In fact, the first para of the "attitudes and interpretation" section is a fairly reasonable (albeit brief) summary of the early unease at the use of renormalization.
On the other hand, what I was questioning is whether the last ten words of that paragraph (and the link to Chris Oakley's personal webpage) should be there. In fact, I'm sure they shouldn't be, for the reasons outlined above: his work has not been published, and in fact has been rejected by peer-review journals. That's what I meant by "his work is not really notable enough to include."
I could continue to discuss the specific details but please tell me why I need to---there's no obvious reason to include the link.--Jpod2 11:23, 26 September 2006 (UTC)
I probably misunderstood you.. I'm not into Straw men. Thank you for clarifying. Zargulon 12:05, 26 September 2006 (UTC)
No problem. Sorry if I sounded a little terse, above. I guess if there is no objection I shall remove the link. All the best--Jpod2 12:16, 26 September 2006 (UTC)

## Renormalization interpretations

I have just identified the fact that an anonymous user (Jpod2) has removed the link to my web page. Apart from being anonymous, there is a clear lack of due diligence here, as even a cursory reading of the QFT section of my web site would show that my work on quantum electrodynamics was published in Physica Scripta in 1990. I cannot see the point in arguing, though, especially as dissenting views are no longer tolerated in QFT research. Dirac and Feynman's words on renormalization have never been heeded less than they are today. But if people really want to know what it amounts to, they can find Dirac's and Feynman's views easily enough, and a simple internet search will find my web site. Chris Oakley 08:43, 30 September 2006 (UTC)

Dear Chris. Firstly, I think anonymous user' on wikipedia usually refers to someone who doesn't log in with a user ID and maintain that same identity. That is not the case for me. Relatively few wikipedia users reveal their personal details, but having a username means that you can check my contributions and assess their quality accordingly. If calling me anonymous' is somehow meant to indicate my contributions are of a lower than required standard, well I believe that misses the mark. My apologies if you were merely pointing out that my personal details are not on the site, but if so I think that's irrelevant.
Secondly, I am not an expert on WP, but I believe I did more than many physics experts on this site would do. First by conducting the debate above, and then leaving it for a few days before removing the link. Many people would have simple erased the link without discussion. You make it sound as if I bypassed all the rules. I think I was quite polite and fair.
I remembered reading your page quite thoroughly a few months ago, but I hadn't remembered that one of the papers was published in Physica Scripta, so I apologise for that. However, I did remember that a number similar papers in various forms had been rejected by major physics journals. Looking these up now, I see that they were Physics Letters B, Nuclear Physics B, Z. fur Physik C and Physical Review D. Surely this casts some reasonable doubt on the papers in question? I'm not sure what the WP policy is in such a situation.
I could go on to discuss my own reasonable doubts about the physics of your ideas, but I'm not sure this is the right forum. My opinion is that your ideas simply are not notable enough to appear in prime position on the WP page, directly following the views of Feynman. There must be many people who have criticised renormalization, and surely we must include only the most noteworthy. We have done that.
I'm sorry if this discussion seems harsh, but I've tried to be fair. WP is not the forum to exhibit `tolerance' in QFT research---it is not about original research at all. It should just reflect the orthodoxy and notable dissenting views. If other physicists disagree with me, I'll be happy to concede to the majority. If we would link to anything it should be the online paper abstract, not to Chris Oakley's webpage. But let me emphasise that if we devote only a single paragraph to these criticisms, then I think the views of Feynman and Dirac adequately cover the necessary ground. --Jpod2 10:48, 30 September 2006 (UTC)
I have to concur with Jpod2 in this case. --Pjacobi 11:40, 30 September 2006 (UTC)
My opinion is that somewhere should have been found on the page for the link to Chris Oakley's website to remain, not on the grounds that his research is notable, but rather because his webpage provides a useful historical overview and clearing centre for these issues. I don't think that JPod2 breached etiquette in removing the link, but I don't agree with its removal. At very least it should have been replaced with a similar site of better notability/quality (although I don't know of one). I also don't feel comfortable characterizing the opinion that renormalization is difficult to justify according to the standard paradigm of mathematical physics as "dissenting".. it's not as if anyone's taken a poll. My personal impression has been that most people use renormalization in QFTs because it works, and are more than happy to acknowledge that it still lacks a thoroughly convincing interpretation. Zargulon 16:00, 30 September 2006 (UTC)
Dear Zargulon, I appreciate and accept your opinion. Possibly we will just have to agree to disagree, but never mind :) Firstly, I'm not sure about the justification of this link as an historical overview. For one, such an overview would be more appropriate if it were by an established scientist or historian of science, and published. I suppose that there are indeed books describing the historical development of QFT, which we could reference. There is already a ref for Feynman's statement, isn't there?
Moreover, my personal assessment is that Chris' overview is strongly POV in places, which is fine, but I don't think that we should link to it as if it were an NPOV extension of Wikipedia. If you want more detail on these issues then perhaps the section itself should be expanded? But, I don't think we can start linking to personal websites in lieu of adding content to WP.
Finally, as far as "dissenting" goes...I think i was using the same language as Chris Oakley in his comment above. My impression and opinion is that the vast majority of theoretical physicists and phenomenologists do not feel at all uncomfortable with the use of renormalization and the RG. Perhaps "dissenting" is not the best word, but the idea that it is important to develop a description of particle physics without renormalization is far from the mainstream. Do we agree on this? This is reflected in the description in any modern textbook on particle physics or QFT, I believe. All the best, and thanks for contributing to the discussion. --Jpod2 16:41, 30 September 2006 (UTC)
I did a very shallow search for notable researchers who may still have an axe to grind with renormalization, but e.g neither this 1994 "historical review" by Bert Schroer nor that recent overwie by Klaus Fredenhagen and Karl-Henning Rehren would IMHO count as such. --Pjacobi 17:21, 30 September 2006 (UTC)
There is room for more WP content on Axiomatic quantum field theory, but probably this stuff belongs on that separate page.
What follows is not NPOV, but I can paraphrase what well-known theoretical physicist told me once: "axiomatic quantum field theory has only proved one statement with physical implications in QFT. And that turned out to be wrong". He was half-joking :) But seriously, I think that if anyone wants to add content on AQFT it would be worthwhile. --Jpod2 21:32, 30 September 2006 (UTC)
I was perhaps unclear. There was nothing to be found in those papers. I've guessed, if at all, the AQFT guys may have written a healthy tirade against renormalization. But I didn't find any. --Pjacobi 11:01, 1 October 2006 (UTC)
Ah, I see what you mean. Such a reference might well be apprpriate if it can be found--Jpod2 19:54, 1 October 2006 (UTC)
Jpod2, interesting.. The majority of theoretical physicists and phenomenologists certainly use renormalization freely and regularly as a standard tool without reference to any interpretative discussion. I'm not sure anyone suggested otherwise.. but "mainstream"? Would you say that e. g. philosophers of science were outside the "mainstream" because they studied difficulties in interpretation in scientific theory, or the scientific process itself, which practitioners of science don't address in their everyday work/publications? Rather than a non-mainstream group, I see them more as a separate community (whose contributions are substantially informative to this article). Zargulon 17:29, 30 September 2006 (UTC)
Hi Zargulon. I'm not sure, but maybe you've misinterpreted my comments above. What I meant was that *within* theoretical physics, any physicists who work on doing QFT without renormalization are well outside the mainstream. Do we agree on this? I agree the philosophy of science is quite a different community.
If someone wants to contribute well-written NPOV content on these subjects that would be very interesting and welcome. I stand by my comment that we should not simply link to POV websites in lieu of adding content to wikipedia. Agreed?
Incidentally, I believe that physicists have a much better understanding of the interpretation of renormalization and the RG than there was 30-40 years ago. But the specific issue under discussion was whether the link to the website was appopriate. For reasons of non-notability, I think not. All the best--Jpod2 21:26, 30 September 2006 (UTC)
I'm not sure anyone has disputed the most recent version of your "mainstream" comment, but I don't see that it has any bearing on whether or not the link should be included. I accept that Chris Oakley's site contains some original research and material presented in a non-neutral way, but I still think it should be linked to for reasons stated above. It is actually completely normal in Wikipedia to do this, provided adequate care is taken to describe the site accurately within the WP article. Zargulon
Dear Zargulon, there was only one sense of "mainstream" I ever used. There was no "recent" or for that matter "earlier" version, and if your implication was that my position has not been consistent, I don't appreciate it. All I did above was to clarify my original meaning, and my only reason for mentioning it in the first place was in response to Chris' use of "dissenting". As I said, WP should reflect the orthodoxy (mainstream) and notable dissenting views (non-mainstream). My only dispute has been that Chris' website is non-notable, which from above you seem to agree with.
I don't think you have addressed my main concern, which is that to link to Chris' website in this way would be essentially extending WP into a domain where we have no control to edit it. It says that on WP we cannot be bothered to add appropriate content. If you do want more content on the historical development of QFT, and in particular attitudes to renormalization, there is no reason why there cannot be more in this article. Or even better in History of quantum field theory.
If you think there should be a reference for further reading, I would agree with you. But, this should ideally be a reference to a work by an established historian of science, published. Why is this controversial? Moreover, at the bottom of the article History of quantum field theory there are already a number of such references! Did you look there? Are they inappropriate, somehow?
I don't understand why we need to add to these references a non-notable, POV, web-based reference which includes original research (all of which you acknowledge are the case with Chris' site). All the best--Jpod2 09:51, 1 October 2006 (UTC)
Well, the question that I was addressing was "should it be removed", whereas you are treating your own removal of it as a fait accompli and are are addressing the different question "should it be added". I'm not sure this is entirely transparent behaviour, although doubtless done in good faith. I don't agree that Chris' site is a POV website. Rather it is a website which includes POV; it also includes non-POV. I'm not sure anyone has called the history links you are referring to "inappropriate", but I feel Chris' site provides something that they do not, and I think the implication that interpreting renormalization is a purely historical issue, is begging the question. I was happy for Chris' site link to be seen as a placeholder until more authoritative material is provided, but I feel that deleting it was wrong. Zargulon 10:15, 1 October 2006 (UTC)
Dear Zargulon. As you have agreed above, I did not breach any WP etiquette by removing the link. I believe I was quite polite, and fair. I also think that if the link were currently on the page, my arguments would be good reasons to remove it. Of course, it is your prerogative to edit the page, and put the link back. In a way I'm surprised you didn't present these arguments above, *before* I removed the link.
Moreover, I am not begging the question by treating this as an historical issue; you yourself introduced it as such by saying:
"My opinion is that somewhere should have been found on the page for the link to Chris Oakley's website to remain, not on the grounds that his research is notable, but rather because his webpage provides a useful historical overview and clearing centre for these issues"
I'm actually not sure what you mean by "clearing centre for these issues", so maybe I focussed too much on your historical comment. Nevertheless, you introduced the argument that the website should be included as a historical reference, not me, and in response I explained that WP already has references to a number of scholarly works on the history of QFT.
I also said above that Chris' website was "strongly POV in places". I'm sorry if I misrepresented your opinion by calling it a POV website. But since we would have no control over which parts of the content people read, I think the distinction is not so important in this context.
I seem to be repeating my points, but let me summarise one last time:
(1) As an historical reference on the development of QFT, Chris' website is non-notable. There are already published books by established historians on this subject referenced in WP. I think you must ask yourself what *precisely* does Chris' website add to these.
(2) As current research on alternatives to renormalization in QFT, Chris' website is non-notable. One of his papers was published in 1990, but after rejection from four main physics journals.
(3) As a link from WP to additional content, Chris' website is inappropriate. It contains some strong POV, and moreover we cannot edit it as part of the WP project. If some of the NPOV content were to be included here in Renormalization or at History of quantum field theory I think that would be a different matter.
For these reasons, I think it is inappropriate for WP. I don't know what more I can say. If you think it would represent concensus, include the link. But I don't think you have addressed the points above.--Jpod2 10:46, 1 October 2006 (UTC)
Addressing your points explicitly: I don't feel that 1 and 2 are particularly relevant to the question of the link. 1) seems yet again to be based on the premise, which I disagree with (and maybe you do too, it's unclear to me) that interpretation of renormalization is of purely historical interest. Chris' site synthesizes sociology of the physics community, history and philosophy; this holistic approach is both informative and absent from the page as it stands. 2) I'm not sure anyone suggested that Chris' site should be included on the grounds of Chris' research or publications into alternatives to renormalization into QFT, although casting aspersions on a paper on the grounds that it was rejected before being accepted, seems like poisoning the well to me. 3) deals with the pertinent question of what qualifies or disqualifies a link from being tolerable, and I think we simply have different views on this. I don't think that a consensus has been established, and as such I don't see any point in reverting your removal. It is enough, for me, that our discussion is a matter of record here. I simply think that, although some of your arguments had merit, removal in this case was on balance destructive; the discussion that Chris' site represents is significant enough despite its shortcomings, that it is vastly better include the link than to relegate the discussion on interpretation to "history of quantum field theory". Zargulon 12:00, 1 October 2006 (UTC)
Dear Zargulon, I emphasise again that it was you who presented the argument that the link be included as an historical reference. It was not my premise, and I did not aim to relegate this discussion to a discussion about history---you yourself introduced that argument for inclusion of the link, and I tried to rebut it. It seems disingenuous to characterise this as my begging of the question, since I was basing my answer on *your* premise. I hope this adequately explains (1).
(2) was in response to Chris' own comment above, about his published paper. I shan't comment further on the paper as it seems unnecessary, since neither of us believe the research is notable enough to include on its own merits. (3) is perhaps the main point of debate between us. I think the disadvantages outweigh the advantages of inclusion. You disagree. It is your opinion that the site is informative, and moreover that its advantages outweigh the non-notability, the elements of POV and the promotion of original research. Perhaps in time other physicists will comment, and we can take things from there. All the best, and thanks for conducting the debate in civil manner. --Jpod2 12:21, 1 October 2006 (UTC)
Cheers, same to you. Zargulon 12:27, 1 October 2006 (UTC)
Zargulon, I am not really arguing with Jpod2. Insofar as my QFT work has never been cited, Jpod2 is correct in saying that it is - according to the Wikipedia definition at least - "non-notable".
Although it may (perhaps justifiably) be construed as self-promotion, the link to my web page did at least show that not everyone is convinced by renormalization, and without it there ought, in the interests of balance, be a little more about the sceptics' views. In this regard, I suggest the full Feynman quote, plus something from Dirac and possibly Landau as well. Chris Oakley 19:35, 1 October 2006 (UTC)
Dear Chris. Thanks for reading what I said and not taking offence. I found your website an interesting read, but for the reasons above just don't think it appropriate content for a link from wikipedia.
I think your suggestions of a bit more from Feynman, Dirac and Landau make sense. Why don't you go ahead and begin the edit?--Jpod2 19:45, 1 October 2006 (UTC)
Jpod2, I will try to make the edit this week. Your comments, by the way, are only reflecting the majority view. Chris Oakley 08:20, 2 October 2006 (UTC)
Sceptical views of Dirac and Feynman added. Chris Oakley 09:20, 9 October 2006 (UTC)
The views of Dirac and Feynman are appreciated, but as the article currently reads, there seems to be a misleading implication that their concerns about renormalization's mathematical legitimacy were satisfactorily addressed by later empirical validations of the technique in statistical mechanics. Djcastel 16:21, 4 December 2006 (UTC)
It is true - Dirac and Feynman never felt that the problem had been satisfactorily solved. I have therefore added words to point this out. Cgoakley 13:36, 5 December 2006 (UTC)

## renormalization in math?

I heard that renormalization is used for computing the Feigenbaum logistic constants, a pure math topic, not physics. Should that go in the renormalization article? I was hoping to find an explanation here or at Feigenbaum constants. 75.62.7.22 04:03, 24 April 2007 (UTC)

## Problem with a reference

I am quite suspicious with the following reference : "A New Approach to Renormalization, Using Zeta regularization" (http://arxiv.org/abs/math/0402259). It has been withdrawn by arXiv administrators because of fraudulently claimed institutional affiliation and status. And to my opinion the preprint is quite poor and irrelevant, compared to other references.

Therefore I suppressed it.

Damien

Let me add that many links given in reference are no longer available (e.g. papers by Rivasseau and Zinn-Justin).

The only "New Approach to Renormalization" that makes any sense to me is to stop doing it altogether. But even if one accepts it, Zeta function regularization is hardly a canonical approach and certainly not worth more than a footnote Cgoakley (talk) 08:26, 26 February 2008 (UTC)
Now 85.85.104.70 (talk) has added an unformatted line: "Zeta regularization applied to divergent integrals}} General Science Journal [1]". It looks like a violation of Wikipedia:V#SELF, so I removed it. — Pt(T) 17:11, 30 April 2010 (UTC)

## Delisted from GA

In order to uphold the quality of Wikipedia:Good articles, all articles listed as Good articles are being reviewed against the GA criteria as part of the GA project quality task force. While all the hard work that has gone into this article is appreciated, unfortunately, as of February 25, 2008, this article fails to satisfy the criteria, as detailed below. For that reason, the article has been delisted from WP:GA. However, if improvements are made bringing the article up to standards, the article may be nominated at WP:GAN. If you feel this decision has been made in error, you may seek remediation at WP:GAR.

GA review – see WP:WIAGA for criteria

1. Is it reasonably well written?
A. Prose quality:
B. MoS compliance:
As with a number of highly technical subjects, this article relies heavily on jargon. This is a problem because undefined jargon tends to cloud meaning, even between those educated in the field, as not all regions use the terms in precisely the same way. Additionally, the article's lead should be accessible to wikipedia's general audience, as should new sections on history and relavance. For more information, see wp:LEAD wp:JARGON and wp:Make technical articles accessible.
2. Is it factually accurate and verifiable?
A. References to sources:
B. Citation of reliable sources where necessary:
The article does not provide any in-line citaitions (beyond attributing the two quotes). I did read the discussion above regarding how "in-line references are unwanted and unnecessary in in overview articles about established topics in physics" but unfortunately this is counter to the accepted consensus of wp:CITE and the good article criteria. Less crucially, the article uses both Harvard and cite.php style references when a single style should be used throughout.
C. No original research:
Without inline references to source texts, the equations and derivations appear to be original Wikipedia research.
3. Is it broad in its coverage?
A. Major aspects:
Specific sections on history and relevance should be included. This information seems to exist already, but not in a style accessible to a general audience.
4. Is it neutral?
Fair representation without bias:
5. Is it stable?
No edit wars, etc:
6. Does it contain images to illustrate the topic?
A. Images are copyright tagged, and non-free images have fair use rationales:
B. Images are provided where possible and appropriate, with suitable captions:
As some images have been tagged with figure numbers, would it not be best if they all were?
7. Overall:
Pass or Fail:

--jwandersTalk 23:23, 25 February 2008 (UTC)

## Meaning unclear to a mathematican

Under Zeta regularization and renormalization, the article states:

Julian Schwinger discovered a relationship between zeta function regularization and renormalization, using the asymptotic relation:

${\displaystyle I(n,\Lambda )=\int _{0}^{\Lambda }dp\,p^{n}\sim 1+2^{n}+3^{n}+...+\Lambda ^{n}=\zeta (-n)}$

as the regulator ${\displaystyle \Lambda \rightarrow \infty }$.

[According to the above Talk section "Zeta function regularization", it appears that this section was at one point removed from the article, but it has now been reinstated, perhaps in revised form.]

I don't know if this makes sense to a physicist, but to a mathematician it appears to be nonsense, since the finite sum 1^n + 2^n + 3^n +...+Λ^n approaches infinity as the number of terms approaches infinity -- for n >= -1.

The article doesn't use the word "limit"; it instead uses the locution "= as", which is meaningless to a mathematician. And, it doesn't specify which range of n it is speaking of.

From later mentions of zeta values at negative odd integers, it appears n above is indeed intended to be positive. The Dirichlet series for zeta(s), which is Sum{n=1..oo} 1/n^s, however, converges only in the range Re(s) > 1, which for "integers" n corresponds to 1^n + 2^n + 3^n + . . . only for n < -1 -- in contrast to the text of this section.

So to this mathematician, it is a mystery what connection this series has with zeta(s) in the range of s where the series is divergent.

Is there any chance that someone knowledgeable in this field could re-express this section in standard mathematical language -- carefullly -- so that it can be understood by people other than physicists?

(Wider readability might also cause this article to be evaluated more highly by the readers who formerly could not understand it.) Thanks.Daqu (talk) 20:51, 24 May 2008 (UTC)

Daqu the sum 1+2+3+4+5+6+7+8+9+............ can be 'regularized' to give a finite limit (see zeta regularization or Ramanujan resummation)for example 1+23+4+....=-1/12 and 1+2+4+8+16+...=0, perhaps the problem is the 'language' used by the contributor ,this part of article should be merged in zeta function regularization —Preceding unsigned comment added by 161.67.109.99 (talk) 15:08, 5 June 2008 (UTC)

161.67.109.99, your statement is incorrect. ${\displaystyle \sum _{i=1}^{\infty }i=\infty }$, and no amount of "regularization" can change this Cgoakley (talk) 13:26, 8 June 2008 (UTC)
Exactly right, Cgoakley. What Ramanujan did is take the expression 1+2+3+... and interpret it as the zeta function evaluated at s = -1, which is nonsense from a rigorous standpoint (since the Dirichlet series for zeta(s) is the summation over n = 1,2,3,... of 1/n^s but this series converges only for Re(s) > 1). If one knows how to extend the zeta function to the entire complex plane (other than s = 1), then it does indeed turn out that zeta(-1) = -1/12. But that is not the same thing as saying that the quoted series 1+2+3+... = -1/2 !!!
Ramanujan, as brilliant as he was, did not -- at least when he wrote that -- understand modern mathematical rigor.Daqu (talk) 23:57, 8 June 2008 (UTC)
Agreed. But how can someone who makes such elementary errors be called "brilliant"? Cgoakley (talk) 09:37, 11 June 2008 (UTC)

Because Cgoakley , zeta regularization made by Ramanujan Euler and others given correct results , of course it can be considered a nonsense but this technique is currently adopted as 'fair' see Casimir Effect or the book by Elizalde 'Zeta regularization techniques with application' even S. Hawking uses it in an article about path integrals. —Preceding unsigned comment added by 161.67.109.102 (talk) 09:00, 12 June 2008 (UTC)

Ah yes, I remember this: people a lot smarter than me say it is alright, so it must be alright. I often had to deal with form of reasoning when I was a graduate student. Unfortunately, I am no longer a graduate student, and am therefore no longer required to tow any party line. Obviously these people are well aware of the fact that they are violating basic rules of mathematics, but they want people to regard the contradictions as lovable foibles. Personally, I do not see it. ${\displaystyle \sum _{i=1}^{\infty }i=\scriptstyle {-{1 \over 12}}}$, for example, is just wrong, and anyone who writes it should just be made to sit in the corner with a dunce cap on their heads. Cgoakley (talk) 12:50, 12 June 2008 (UTC)

In mathematics the statement that the sum of an infinite series is equal to a certain number has one and only one meaning. Any other interpretation is unequivocally wrong.
Many subjects can have statements open to multiple conflicting interpretations. Mathematics is not one of these subjects.
Mathematics is a precise language where, unlikely the case of Humpty Dumpty in Lewis Carroll, words and notation do not mean whatever someone wants them to mean.
On the other hand, if Ramanujan regularization is a different way of taking the terms of an infinite series as input and obtaining a number as an output, then of course there is nothing wrong with that at all. But then it is necessary to say that "the Ramanujan regularization of 1+2+3+ . . . +n+ . . . = -1/12".
This is entirely different from insisting that, because the series can have Ramanujan regularization applied to it, the sum of the series 1+2+3+ . . . +n+ . . . "is" -1/12 .
That is like insisting that 3+4 "is" 2 because the sum can be intepreted modulo 5. That would be complete nonsense, just as is the claim that the sum of the positive integers "is" -1/12.
If you do not understand the basic principle that mathematical language is precise, then you should not be editing articles about mathematics.Daqu (talk) 06:15, 4 November 2010 (UTC)

Hello friends!

Recently I published a very comprehensible preprint (arxiv:0811.4416) where I explained why the perturbative corrections to the fundamental constants arise, why the renormalization procedure works, and how to rewrite the QED and gauge QFT theories in order to avoid these logical and mathematical complications. Enjoy!

Vladimir Kalitvianski. —Preceding unsigned comment added by 90.37.240.75 (talk) 18:21, 29 November 2008 (UTC)

## Quantum correction

Is the term quantum correction synonymous with renormalization? 70.247.169.197 (talk) 18:09, 14 August 2010 (UTC)

This does not appear in the article so the context is missing. Guessing, I would say no. Quantum corrections to me means corrections from loops (in perturbation theory) or higher order corrections (in general) or off-shell particles correction (also general), which are all similar but not identical concepts. Setreset (talk) 11:23, 22 August 2010 (UTC)

## General comment

The article does not focus enough on renormalization. It contains only 2 sentences on the process itself, under "Renormalization schemes". This is also reflected in the lead section which has a limited and unhelpful definition (assumes non-continuum regularization, besides not defining "continuum"). The latter I tried to improve. Setreset (talk) 11:22, 22 August 2010 (UTC)

Also, it isn't sufficiently understandable and isn't readily understood by technical but non-specialist readers. A bit of attention in that area would help. It should be possible to ensure the concepts are better explained in overview without sacrificing technical rigor. FT2 (Talk | email) 02:34, 14 November 2012 (UTC)

## funny statement

"A rigorous mathematical approach to renormalization theory is the so-called causal perturbation theory, where ultraviolet divergences are avoided from the start in calculations by performing well-defined mathematical operations only within the framework of distribution theory. The disadvantage of the method is the fact that the approach is quite technical and requires a high level of mathematical knowledge."

so basically "this (working) method has the disadvantage, that, to use it, you need to know math." odd statement. i don't know if this should be called a disadvantage. maybe one could say it is more "laborious" to use it or something like this. otherwise it could be said of any mathematical method used in physics that it has the "disadvantage that you need to know math" 92.196.116.53 (talk) 22:20, 19 September 2013 (UTC)

## is renormalization an issue only for perturbative methods?

Supposing we have a theory that requires renormalization in order to give sensible results in diagrammatic approaches. Is that renormalization fundamental to the theory, or is it just an "artifact" of the calculation of perturbation expansion? Supposing I had an exact way of solving the theory, would renormalization still play a role? Nanite (talk) 01:20, 9 February 2014 (UTC)

Yes, it is still necessary. Lattice simulations, for example, give a nonperturbative solution to quantum field theories, but many quantities (such as propagators) still diverge when taking the lattice spacing to zero. Furthermore, the connection between bare and physical parameters (such as masses) remains nontrivial, and renormalization has to be used to establish the relationship. MuDavid (talk) 03:56, 5 March 2015 (UTC)

## "Protection"

I keep seeing the terminology "protected" as applied to renormalization, but I'm not sure what it means. Is this article an appropriate place to explain this terminology? — Preceding unsigned comment added by 70.247.166.192 (talk) 03:28, 26 August 2015 (UTC)

It means there exists something (usually a symmetry) making it unnecessary to renormalize the operator under consideration, i.e. the operator is protected from renormalization. I suppose it could be nice to note this somewhere in the article. MuDavid (talk) 08:28, 23 October 2015 (UTC)