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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)
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)
surely for the scientific american level crowd, a better intro can be provided, eg what the heck is a continuum ? etc etc Cinnamon colbert ( talk) 20:04, 15 September 2008 (UTC)
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)
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:
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)
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)
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:
as the regulator . Based on this, he considered using the values of to get finite results. Although he reached inconsistent results, an improved formula by Hartle, J. Garcia and E. Elizalde includes
where the B's are the Bernoulli numbers and
This reduces every ultraviolet divergence to the case 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 For infrared divergences, one may just put 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 one has, they all can be expressed as a linear combination of and (for the case of , 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.
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
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
Srik e it( talk ¦ ✉) 14:56, 27 May 2006 (UTC)
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)
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)
Renormalization -- see also: Fudge factor
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)
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).
In order to uphold the quality of
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-- jwanders Talk 23:23, 25 February 2008 (UTC)
Under Zeta regularization and renormalization, the article states:
Julian Schwinger discovered a relationship between zeta function regularization and renormalization, using the asymptotic relation:
as the regulator .
[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)
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)
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)
Is the term quantum correction synonymous with renormalization? 70.247.169.197 ( talk) 18:09, 14 August 2010 (UTC)
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)
"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)
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)
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)
The greater the degree of renormalization, the more time that Feynmanian diagram version lasts. Of course all the infinite possible diagrams are extant, but simply for less time because unnecessarily complex diagrams (or particle pathways) are probabilistically less significant. Renormalization is actual though and bends measurably the paths of the particles at all scales. The graviton is simply a renormalization polariton (same concept). — Preceding unsigned comment added by 2A02:587:4102:CF00:1963:F284:B24D:197C ( talk) 06:24, 8 October 2016 (UTC)
There a several articles that link radiative correction to this article, yet there is no discussion of that term here? I'm guessing there probably should be, and my feeling is that it would be beneficial to have a radiative correction redirect page as well, whether it points here or elsewhere. 75.139.254.117 ( talk) 21:15, 14 March 2017 (UTC)
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Sylvain Ribault ( talk) 19:21, 27 October 2018 (UTC)
I can't think of any reason there should be an image of a penguin behind the penguin diagram. Showing that the penguin diagram looks kind of like a penguin is distracting to the rest of the article and pointless. — Preceding unsigned comment added by 63.163.123.182 ( talk) 19:35, 6 December 2018 (UTC)
Not necessary but cute, please keep. -- 77.191.179.90 ( talk) — Preceding undated comment added 03:18, 30 January 2024 (UTC)
Called by people who deem it a means to avoid causally important open questions. — Preceding unsigned comment added by 2A02:587:410A:2A66:B176:F6E0:296B:D53E ( talk) 16:18, 21 June 2020 (UTC)
Dear all,
the article presently has a strong focus on renormalization in the context of high-energy physics. However, the term renormalization is used in physics in a broader scope beyond high-energy physics and I think the introduction should reflect that. There has also been a lot of debate on this talk page whether the introduction is accessible to technical but non-specialist readers. I think explaining the concept more broadly would potentially allow explaining some things more simply without having to delve into the complexities of the high-energy physics context. Nevertheless, changing the introduction is such a way would clearly clash with the remainder of the article which almost exclusively focuses on the high-energy physics context. Therefore, I would like to first discuss the change here before doing an actual edit. I would be very happy about some feedback.
My proposal for an broader introduction that is hopefully more accessible is the following:
Renormalization refers to a change of parameters of a physical theory that captures the effects that "microscopic" processes within the theory have on "macroscopic" processes. The distinction between "microscopic" and "macroscopic" processes is that the former occur on a smaller length scale than the latter. Given a parameter renormalization, the original theory can be turned into an effective theory for the macroscopic processes by discarding the microscopic processes from the original theory and and applying the parameter renormalization.
As an example, consider a capacitor with a dielectric. Charges on the capacitor plates will polarize the dielectric. Consequently, the resulting electric field between the capacitor plates will be weaker than the field that would be created by the charges alone. The parameter controlling the strength of the electric field created by charges is the vacuum permittivity. To describe the above effect, we have two options. We can work with a full microscopic theory that explicitly models the microscopic dipoles inside the dielectric or we can choose to only model the "macroscopic" charges on the capacitor plates. If we choose the second option, we have to renormalize the vacuum permittivity to account for the presence of the dielectric. The renormalization is the replacement of the vacuum permittivity by the dielectric's permittivity.
In the context of statistical mechanics and quantum field theory, effective theories and their renormalized parameters for macroscopic processes occuring on length scales that are larger than a so-called cut-off can be formally derived. Calculating the evolution of the renormalized parameters as the cut-off is continuously varied is the subject of the Renormalization group.
Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Renormalization is distinct from regularization, another technique to control infinities by assuming the existence of new unknown physics at new scales.
Jascha Tempeler ( talk) 07:33, 13 September 2021 (UTC)
This infuriating article suffers from a common Wikipedia malady: the author(s) assume the reader is already conversant with the topic. YOU JUST DONT DEFINE THE TERMS! I sought this article because I wondered: “what is renormalization?” No answer here. The first paragraph tells me it’s used in science, blah blah. BUT DOESNT SAY WHAT THE TERM IS!” Let me help the author(s): start out: “Renormalization is…” THEN DEFINE THE WORD!! Geez! Is that so hard to understand? 98.183.27.92 ( talk) 01:40, 4 January 2024 (UTC)
Ok, there is a renormalization tutorial here and the videos are on youtube. I haven't tried to watch any and I'm a bit suspicious that one of the topics is the Krohn-Rhodes theorem which is about semigroups. Regarding OP's complaint (disclosure: I took a fair number of math classes in school but not much physics) I think maybe there is a difference in culture. Math and physics are both huge, deeply connected topics, but things were simpler in the Newtonian era. Studying physics seems to start with Newtonian mechanics and then add relativity, quantum mechanics, relativistic quantum mechanics, QFT all layer by layer, keeping the whole picture in view at all times, so they don't discuss renormalization without bringing all the rest of physics with it. Math on the other hand tends to break out its ideas in isolation so you study them one at a time before the big picture emerges. So in math it is easier to say (McMullen p. 98) "The map is renormalizable if there are open discs U and V in such that bla bla bla... the choice of a pair as above is a renormalization of ." That doesn't tell you what renormalization is good for or how to use it, but it at least precisely tells you what it is. The chapter also opens more informally, "Renormalization is a tool for the study of nonlinear systems whose essential form is repeated at infinitely many scales."
I wonder if it's possible for the article to include a worked-out example from physics, like maybe calculation of the Lamb shift, which apparently was one of the original applications of renormalization. 2601:644:8501:AAF0:0:0:0:2034 ( talk) 21:44, 29 January 2024 (UTC)
This is interesting: "Such divergences arise because the coefficients in these series are products of generalized functions, i.e. the object is, in general, not well defined." Generalized function means objects like the Dirac delta "function" which isn't a function in the usual sense. So getting rid of the divergences is complicated. I've heard that QFT has been formalized in terms of rigged Hilbert spaces (spaces of generalized functions) and I guess that explains why. I don't know enough math to understand this. Generalized functions are a messy mathematical formalism developed in the 1950s, sometime after QFT, and I think physicists don't really care about them, preferring to treat them like regular functions plus a few tricks. 2601:644:8501:AAF0:0:0:0:2034 ( talk) 01:12, 30 January 2024 (UTC)
![]() | 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 |
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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)
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)
surely for the scientific american level crowd, a better intro can be provided, eg what the heck is a continuum ? etc etc Cinnamon colbert ( talk) 20:04, 15 September 2008 (UTC)
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)
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:
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)
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)
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:
as the regulator . Based on this, he considered using the values of to get finite results. Although he reached inconsistent results, an improved formula by Hartle, J. Garcia and E. Elizalde includes
where the B's are the Bernoulli numbers and
This reduces every ultraviolet divergence to the case 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 For infrared divergences, one may just put 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 one has, they all can be expressed as a linear combination of and (for the case of , 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.
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
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
Srik e it( talk ¦ ✉) 14:56, 27 May 2006 (UTC)
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)
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)
Renormalization -- see also: Fudge factor
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)
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).
In order to uphold the quality of
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GA criteria as part of the
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-- jwanders Talk 23:23, 25 February 2008 (UTC)
Under Zeta regularization and renormalization, the article states:
Julian Schwinger discovered a relationship between zeta function regularization and renormalization, using the asymptotic relation:
as the regulator .
[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)
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)
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)
Is the term quantum correction synonymous with renormalization? 70.247.169.197 ( talk) 18:09, 14 August 2010 (UTC)
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)
"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)
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)
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)
The greater the degree of renormalization, the more time that Feynmanian diagram version lasts. Of course all the infinite possible diagrams are extant, but simply for less time because unnecessarily complex diagrams (or particle pathways) are probabilistically less significant. Renormalization is actual though and bends measurably the paths of the particles at all scales. The graviton is simply a renormalization polariton (same concept). — Preceding unsigned comment added by 2A02:587:4102:CF00:1963:F284:B24D:197C ( talk) 06:24, 8 October 2016 (UTC)
There a several articles that link radiative correction to this article, yet there is no discussion of that term here? I'm guessing there probably should be, and my feeling is that it would be beneficial to have a radiative correction redirect page as well, whether it points here or elsewhere. 75.139.254.117 ( talk) 21:15, 14 March 2017 (UTC)
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Sylvain Ribault ( talk) 19:21, 27 October 2018 (UTC)
I can't think of any reason there should be an image of a penguin behind the penguin diagram. Showing that the penguin diagram looks kind of like a penguin is distracting to the rest of the article and pointless. — Preceding unsigned comment added by 63.163.123.182 ( talk) 19:35, 6 December 2018 (UTC)
Not necessary but cute, please keep. -- 77.191.179.90 ( talk) — Preceding undated comment added 03:18, 30 January 2024 (UTC)
Called by people who deem it a means to avoid causally important open questions. — Preceding unsigned comment added by 2A02:587:410A:2A66:B176:F6E0:296B:D53E ( talk) 16:18, 21 June 2020 (UTC)
Dear all,
the article presently has a strong focus on renormalization in the context of high-energy physics. However, the term renormalization is used in physics in a broader scope beyond high-energy physics and I think the introduction should reflect that. There has also been a lot of debate on this talk page whether the introduction is accessible to technical but non-specialist readers. I think explaining the concept more broadly would potentially allow explaining some things more simply without having to delve into the complexities of the high-energy physics context. Nevertheless, changing the introduction is such a way would clearly clash with the remainder of the article which almost exclusively focuses on the high-energy physics context. Therefore, I would like to first discuss the change here before doing an actual edit. I would be very happy about some feedback.
My proposal for an broader introduction that is hopefully more accessible is the following:
Renormalization refers to a change of parameters of a physical theory that captures the effects that "microscopic" processes within the theory have on "macroscopic" processes. The distinction between "microscopic" and "macroscopic" processes is that the former occur on a smaller length scale than the latter. Given a parameter renormalization, the original theory can be turned into an effective theory for the macroscopic processes by discarding the microscopic processes from the original theory and and applying the parameter renormalization.
As an example, consider a capacitor with a dielectric. Charges on the capacitor plates will polarize the dielectric. Consequently, the resulting electric field between the capacitor plates will be weaker than the field that would be created by the charges alone. The parameter controlling the strength of the electric field created by charges is the vacuum permittivity. To describe the above effect, we have two options. We can work with a full microscopic theory that explicitly models the microscopic dipoles inside the dielectric or we can choose to only model the "macroscopic" charges on the capacitor plates. If we choose the second option, we have to renormalize the vacuum permittivity to account for the presence of the dielectric. The renormalization is the replacement of the vacuum permittivity by the dielectric's permittivity.
In the context of statistical mechanics and quantum field theory, effective theories and their renormalized parameters for macroscopic processes occuring on length scales that are larger than a so-called cut-off can be formally derived. Calculating the evolution of the renormalized parameters as the cut-off is continuously varied is the subject of the Renormalization group.
Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Renormalization is distinct from regularization, another technique to control infinities by assuming the existence of new unknown physics at new scales.
Jascha Tempeler ( talk) 07:33, 13 September 2021 (UTC)
This infuriating article suffers from a common Wikipedia malady: the author(s) assume the reader is already conversant with the topic. YOU JUST DONT DEFINE THE TERMS! I sought this article because I wondered: “what is renormalization?” No answer here. The first paragraph tells me it’s used in science, blah blah. BUT DOESNT SAY WHAT THE TERM IS!” Let me help the author(s): start out: “Renormalization is…” THEN DEFINE THE WORD!! Geez! Is that so hard to understand? 98.183.27.92 ( talk) 01:40, 4 January 2024 (UTC)
Ok, there is a renormalization tutorial here and the videos are on youtube. I haven't tried to watch any and I'm a bit suspicious that one of the topics is the Krohn-Rhodes theorem which is about semigroups. Regarding OP's complaint (disclosure: I took a fair number of math classes in school but not much physics) I think maybe there is a difference in culture. Math and physics are both huge, deeply connected topics, but things were simpler in the Newtonian era. Studying physics seems to start with Newtonian mechanics and then add relativity, quantum mechanics, relativistic quantum mechanics, QFT all layer by layer, keeping the whole picture in view at all times, so they don't discuss renormalization without bringing all the rest of physics with it. Math on the other hand tends to break out its ideas in isolation so you study them one at a time before the big picture emerges. So in math it is easier to say (McMullen p. 98) "The map is renormalizable if there are open discs U and V in such that bla bla bla... the choice of a pair as above is a renormalization of ." That doesn't tell you what renormalization is good for or how to use it, but it at least precisely tells you what it is. The chapter also opens more informally, "Renormalization is a tool for the study of nonlinear systems whose essential form is repeated at infinitely many scales."
I wonder if it's possible for the article to include a worked-out example from physics, like maybe calculation of the Lamb shift, which apparently was one of the original applications of renormalization. 2601:644:8501:AAF0:0:0:0:2034 ( talk) 21:44, 29 January 2024 (UTC)
This is interesting: "Such divergences arise because the coefficients in these series are products of generalized functions, i.e. the object is, in general, not well defined." Generalized function means objects like the Dirac delta "function" which isn't a function in the usual sense. So getting rid of the divergences is complicated. I've heard that QFT has been formalized in terms of rigged Hilbert spaces (spaces of generalized functions) and I guess that explains why. I don't know enough math to understand this. Generalized functions are a messy mathematical formalism developed in the 1950s, sometime after QFT, and I think physicists don't really care about them, preferring to treat them like regular functions plus a few tricks. 2601:644:8501:AAF0:0:0:0:2034 ( talk) 01:12, 30 January 2024 (UTC)