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Archive 1 |
Ok, I'm going to get the ball rolling by pointing out that there is pretty much no information here. Unfortunately, I don't know enough about Yang-Mills theories to contribute, so I think we really need an expert. StewartMH ( talk) 20:54, 18 April 2008 (UTC)
This voice should be renamed from "Yang-Mills" to "Yang-Mills theory". Pra1998 ( talk) 10:55, 24 November 2008 (UTC)
I have prepared a jpeg file with latex containing Feynman's rules for Yang-Mills theory. I would like to insert this image into this article as it is in need of it. Please, could you help me? Thanks beforehand. Pra1998 ( talk) 11:21, 25 November 2008 (UTC)
I think that any encyclopedia must have an article about Yang-Mills theory. The reason is that Yang-Mills theories describe strong and electro-weak interactions and when these are discussed one is forced to recall them anyway.
About the quality of the article, I am not fully convinced that the B class is the right one. But it is no more at a starting level and I have substantially put forward a well developed scheme to build upon. The aim is to reach a higher level of quality making this article useful both to students and researchers. Of course, any suggestion about is welcome. Pra1998 ( talk) 16:31, 2 December 2008 (UTC)
Yang-Mills theory represents a great mathematical challenge and so also wikipedia should consider as such entering into the WikiProject Mathematics. Pra1998 ( talk) 16:34, 2 December 2008 (UTC)
I take this chance to thank Michael for his intervention. Section about integrable solutions gives no other than an a class of exact classical solutions of Yang-Mills equations and this is always true independently on any theoretical construction one can ever do. -- Pra1998 ( talk) 10:24, 25 February 2009 (UTC)
As you may know, Peter Woit is a critic of science. By "critic of science" one means the same as a movie critic that does not produce any original work by his own but is very active in criticizing other work. This section contains no other than a class of exact solutions of classical Yang-Mills equation and this is plain mathematics without further claim. I could have as well cited the Smilga's book that proposed such solutions and the result would be the same.
The right approach here would be eventually to remove any claim about Frasca's work maintaining the exact solutions of Yang-Mills equations that are true independently on Woit point of view.
Addendum: There is currently, in our community, the idea that an ignored idea is a wrong idea. Of course, this is plainly false as history of physics taught us. Rather, fashions make the path and new ideas may find serious difficulties to affirm. What is really important is that there exist a lot of ideas that are published in physics journals everyday. It is this that makes our field really sane.-- Pra1998 ( talk) 09:21, 26 February 2009 (UTC)
-- Pra1998 ( talk) 08:15, 26 February 2009 (UTC)
Headbomb, sorry for the improper comment and thank you for pointing me this out. I apologize if my sentence implied an offense. I think you hit the point and this was the argument I was making. This is just a class of exact solutions for classical Yang-Mills equations and I think they should be there as also other ones that should be inserted. Of course, there is no harm if this implies removing Frasca ref. and pointing just to Smilga's one.-- Pra1998 ( talk) 10:14, 26 February 2009 (UTC)
If, by "critic of science", you mean well-respected contributor of science, then yes. The characterisation of Peter Woit as a mere "critic of science" is akin to to calling Stanley Kubrick a "film critic." -- Logoskakou ( talk) 15:49, 26 February 2009 (UTC)
On a general note, I'm beginning to wonder if I'm not smelling some WP:MEAT here. A newly registered editor removes material, then an editor inactive for one year replies and heralds the first one as being "really super". Nothing to warrant ignoring WP:AGF at this point, but there's some red flags being raised. Headbomb { ταλκ κοντÏιβς – WP Physics} 16:42, 26 February 2009 (UTC)
The last part of this article has nothing to do with conventional main-stream understanding of Yang-Mills theory. It is purely the work of Marco Frasca, a physicist who appears to have no institutional affiliation (his papers carry his home address) who I suspect is "Pra1998". There is no reference arguing against these ideas since they are completely ignored by the main-stream. This sort of thing should have no place here. Frasca is free to argue for his ideas on his blog, but he shouldn't be doing it by inserting them into Wikipedia entries. —Preceding unsigned comment added by Peterwoit ( talk • contribs) 01:38, 26 February 2009 (UTC)
I don't know much about Wikipedia standards. The bottom line is that the content in question is unconventional speculation due to Frasca, speculation that I don't think anyone else is much interested in or convinced by. Lots of such ideas are published in journals, and then mostly ignored. Personally I don't think they belong on Wikipedia at all, but they certainly don't belong in an entry like this on one of the core ideas of modern physics. Peterwoit ( talk) 01:54, 26 February 2009 (UTC)
I read the section in some details, and while I don't understand one thing about it, it does feels like WP:OR. Especially with sentences like "the infrared theory has been recently formulated" and "the results appear to be in agreement with computations with lattice field theory". I don't know how recent 2006 is in QFT, but this may be too immature to include in WP. Headbomb { ταλκ κοντÏιβς – WP Physics} 17:17, 26 February 2009 (UTC)
I've reverted to the pre-revert war state of the article. Beware of revert wars, as you may be blocked for it. Now that being said (I'm no admin, I'm just warning people that you could very well get banned for this), it is a bit sad that Mr. Woit simply did not explain his position in more details and gave up on the whole thing rather than explain to us how the Frasca/Smigma articles/books are not reliable when it comes to this topic ( see his blog). Anyway, I left a message on his talk page, perhaps he'll come back an explain where Frasca got it wrong and give us some refs. Headbomb { ταλκ κοντÏιβς – WP Physics} 16:57, 26 February 2009 (UTC)
Thanks AJ, couldn't have said it better myself. Peterwoit ( talk) 20:00, 26 February 2009 (UTC)
Dear Headbomb,
Thank you very much for your intervention. People here do not even know how Wikipedia works. -- Pra1998 ( talk) 18:30, 26 February 2009 (UTC)
The pre revert war is the one with Marco Frasca version, so I reverted to that version because otherwise people will NOT be able to judge the material properly. They will have to click on the history of the article, which is already extremely confusing. The dispute warning is enough to make sure one thinks that the information presented can be accurate or not, and is wainting for an evaluation on the talk page. If anyones think it's necessary, move the section for apreciation on the talk page, but please, do not delete it from the main article. Daniel de França ( talk) 12:34, 27 February 2009 (UTC)
The first introductory paragraph implies that the U(1) of SU(2)xU(1) on electroweak theory is the U(1) of QED. This is not the case -the U(1) in electroweak is u(1) hypercharge. —Preceding unsigned comment added by 128.230.72.196 ( talk) 17:04, 12 March 2009 (UTC)
Per the arguments presented by everyone here, consensus is that this is original research, non-notable, and potentially self-publication, I have deleted this section. Headbomb { ταλκ κοντÏιβς – WP Physics} 00:14, 27 February 2009 (UTC)
See also Wikipedia:Suggestions for COI compliance. Headbomb { ταλκ κοντÏιβς – WP Physics} 01:01, 27 February 2009 (UTC)
Headbomb, do you think science is something decided by majority? Before an overwhelming number of people complaining, without a real understanding of the content, you removed it. The point here is that I am not a person who wrote a libel against a part of the scientific community becoming an instantaneous star, with anyhow a poor scientific curriculum, able to move a lot of people against a single one. If this is a serious project you were not.—Preceding unsigned comment added by Pra1998 ( talk • contribs) 13:20, 27 February 2009 (UTC)
It may be relevant to point out that one of the references cited in the disputed section [3] has a significant error in it, despite being published. Namely, in the proof of Theorem 1, the author is assuming that an extremum A for the Yang-Mills action for a special class of connections (namely those in which and all other components vanish) is necessarily an extremum for the Yang-Mills action for all other connections also, but this is not the case (just because , for instance, for A' of this special form, does not imply that for general A'). Since one needs to be an extremiser (or critical point) in the space of all connections in order to be a solution to the Yang-Mills equations, the mapping provided in Theorem 1 has not been shown to actually produce solutions to the Yang-Mills equation (and I suspect that if one actually checks the Yang-Mills equation for this mapping, that one will not in fact get such a solution). Terry ( talk) 20:32, 28 February 2009 (UTC)
Terry, the author assumes that exists a class of solutions that maps Yang-Mills action on the one of a scalar field. You can find that above solution is indeed a solution of Yang-Mills equations. Check Smilga book [4]. Instead to rely on questionable theoretical arguments, take Maple or Mathematica and check it. There is no claim about what you are saying -- Pra1998 ( talk) 11:27, 2 March 2009 (UTC)
Dear Headbomb, you can find good reviews of some Frasca's works here [6], e.g. this MR2345223 (2008f:81084) and this MR2332380 (2008e:81089). If you belong to some recognized institution you should have access to this mathematical database. But here I just entered into this discussion area to answer a wrong affirmation by Terry, a claim that can be easily proved wrong with Maple or Mathematica. I have no interest to defend Frasca's work as you can see from my preceding interventions where I would have removed the refs without problem. The fact that you removed also Smilga's book, well, that is your choice. You removed just plain mathematics but it is your own right.Thank you anyway.-- Pra1998 ( talk) 20:31, 2 March 2009 (UTC)
Headbomb, I give you the exact refs. to look for. If you are not able to cope with scientific databases please ask somebody expert. This is not google, this is a database of American Mathematical Society, well known to people doing research, that gives reviews of papers after publication. Please, ask to a person being an active researcher in a recognized institution.-- Pra1998 ( talk) 07:56, 3 March 2009 (UTC)
I have added some references but DOI numbers do not appear even if they seem correctly inserted. Any help?-- Pra1998 ( talk) 13:34, 5 May 2010 (UTC)
A user from wanadoo.fr added a disputable comment having no value for Wikipedia. I removed as vandalism. This is again the question if new physics results should go on Wikipedia producing such kind of effects. Let me know your view. But adding such a comment in the article rather than the discussion is pure vandalism.-- Pra1998 ( talk) 16:18, 6 November 2010 (UTC)
An anonymous user introduced this:
"Prior to Yang-Mill's publication, Pauli had given a seminar on the same idea but did not publish because he did not believe it would work at the time. When Yang gave his talk, Pauli asked Yang a question which Yang could not answer. Yang's talk ended abruptly. Yang then avoided Pauli even though Pauli tried to reach Yang to discuss the idea in more detail. Yang's behavior led many scientists to question how much Yang had to do with the origination of the idea."
I think this kind of stories should be well supported by proper citations. Does anyone out there know this? —Preceding unsigned comment added by Pra1998 ( talk • contribs) 08:43, 24 November 2009 (UTC)
Michael, sorry for omitting my signature. Just oversight. I tried to use citation needed but it did not seem to work in preview and so I have chosen the bad way.-- Pra1998 ( talk) 16:49, 24 November 2009 (UTC)
't Hooft asked Yang to provide some materials for how he and Mills developed Yang Mills theory. All Yang was able to provide for 't Hooft's " 50 years of Yang Mills theory" were a couple pages from his graduate student days...does that dovetail with above discussion that Yang had actually borrowed Pauli's unpublished idea and got away with it since nobody at that time thought Yang mills was anything significant?
Also, Yang co-published a paper shortly after his Yang Mills with T.D. Lee, where the key argument was anti (against) Yang Mills thoery. So, Yang himself was not convinced about the validity of Yang Mills theory at that time. —Preceding unsigned comment added by 163.166.135.44 ( talk) 01:27, 24 December 2009 (UTC)
There are documents which show that wolfgang Pauli developed in 1953 the first consistent generalization of the five-dimensional theory of Kaluza, Klein, Fock and others to a higher dimensional internal space. Because Pauli saw no way to give masses to the gauge bosons, he refrained from publishing his results formally. Pauli gave talks on the subject and many physicists of the time, including Yang, debated Pauli's unplublished theory.(See "On Pauli's invention of non-abrlian Kaluza-Klein Theory in 1953") —Preceding unsigned comment added by 69.156.210.199 ( talk) 13:50, 27 October 2010 (UTC)
About Pauli in 1953: apparently he compactified a 6-dimensional space and found SU(2) gauge theory (much like Kaluza and Klein toroidally compactified a 5-dimensional space and found U(1) gauge theory). However, Yang and Mills showed how requiring local gauge invariance severely restricts the terms in the Lagrangian. To me, these are very different things: on the one hand Pauli found one SU(2) gauge theory, and on the other hand Yang and Mills showed that it's basically the only reasonable one out there. We can debate forever from where Yang and Mills got their idea, but to me it's clear that the point here is the importance of local gauge invariance, and this is the point Yang and Mills made. —Preceding unsigned comment added by 132.206.126.18 ( talk) 21:24, 15 February 2011 (UTC)
I'm a complete layman in the field, but IMO a lot of formulas are bloated and could be written more concisely in a coordinate-free manner and/or with some intermediate definitions. — Kallikanzarid talk 18:47, 19 February 2011 (UTC)
The lack of any citations in the Mathematical Overview section of the article seems like a bit of a problem; in particular it makes it almost impossible to use the article as a starting point for a review of the mathematics of Yang-Mills theory (as I currently am).
In particular, I'm looking for a citation for Pra1998's edit in 2009 adding the note about the lack of distinction between and upper and lower a indices; this fact seems to be taken implicitly in all books and articles I've found so far and was hoping someone would know a specific source explicitly stating that it is legitimate.
I've also made a post at the reference desk because, being new, I wasn't sure what the best channel was.
https://en.wikipedia.org/?title=Wikipedia:Reference_desk/Science&oldid=648352928#Citation_for_Yang-Mills_Theory_-_Mathematical_Overview — Preceding unsigned comment added by Tjlr2 ( talk • contribs) 18:09, 22 February 2015 (UTC)
Is Yang-Mills theory science or math? They are not the same thing.
The lead says, "Yang–Mills theory seeks to describe the behavior of elementary particles..." which suggests that its developers have intended to provide a mathematical model for this aspect of the physical world - that is, they intend to provide a tool for elucidating a scientific theory of the world.
After providing a précis list of the symmetry groups of the Standard Model, in the 'History and theoretical description' section I read "This may be the reason why confinement has not been theoretically proven, though it is a consistent experimental observation." While as a lay person, I understand that confinement is in fact what has been observed, I don't at all understand what - in the context of a scientific theory of the world - can even be meant by "theoretically proven".
I know that it is common to refer to large parts of mathematics as the 'theory' of this or that, as the Theory of Numbers' and so forth and though I think this is not nonsensical, I am uncomfortable with this sort of construction appearing here, if, as in the lead, 'YM Theory' is intended to be an article describing a scientific theory of the natural world. Theorems are objects of mathematics. Theories - which are always contingent and so are unprovable - are objects of science.
In 1979, during his noted series of popular lectures given at the University of Aukland, New Zealand, Richard Feynman said
How is Feynman's discussion of the EM coupling constant not an example of the inappropriateness of imagining that proving a mathematical theorem or proving the consistency of some assertions in a symbolic calculus is the same thing as 'proving' an assertion about the world? Have I not argued sufficiently for the affinity between on the one hand claims for mathematical (geometric, topological etc.) derivations of α and on the other hand, hope for 'mathematical proof' that confinement is necessary?
Alternately, I understand that this observation is supported by a thirty-five-year-old perspective from a man with a complicated attitude toward 'villozovy' and so on. Is Feynman's view now considered dowdy? Or still just inconvenient? Rt3368 ( talk) 17:03, 25 August 2015 (UTC)
At this date (6/11/2017), it's written "{\displaystyle [A]=[L^{\frac {2-D}{2}}]} [A]=[L^{\frac {2-D}{2}}]" . I think it's 2-\frac{D}{2}, but I could be wrong (my own computation gives this power, and I also think it agrees with the next result, contrary to the given power) — Preceding unsigned comment added by 134.157.64.191 ( talk) 18:23, 6 November 2017 (UTC)
I think that, in agreement with Woit's ideas we should remove all the section. The paper he is questioning is regularly published in a prestigious journal and is a collaboration with a reputable physicist.-- Pra1998 ( talk) 21:52, 27 April 2018 (UTC)
Could we please discuss the passages and parts regarding known or unknown quantities which seem to inflame our anonymous editor so much? I'm afraid I don't know much about theoretical physics, but I'm willing to try to learn. —
Javert2113 (
talk)
15:05, 29 April 2018 (UTC)
There is no need to deal with the complex scientific issues here. Pra1998=Marco Frasca, and my understanding is that Wikipedia policy does not allow people to add references to their own work to Wikipedia pages. Peterwoit ( talk) 14:50, 30 April 2018 (UTC)
I would like to add a new section to this article, with the above section title, following the section "Quantization." My proposed section is below. Are there any objections or suggestions, prior to my doing so?
Studying the physics of Yang-Mills gauge theory requires understanding what happens to Maxwell’s electrodynamics, and U(1) quantum electrodynamics (QED), when Maxwell’s commuting (abelian) gauge fields become non-commuting (nonabelian) gauge fields covariantly transforming, for example, under the compact simple Yang-Mills gauge group SU(N) with NxN Hermitian generators and a commutator typically normalized such that for each . Whereas electrodynamics is a linear theory in which the gauge fields to not interact with one another, Yang-Mills theory is highly nonlinear with mutual interactions amongst the gauge fields.
In flat spacetime, in classical electrodynamics, a gauge-invariant field strength is related to the gauge fields by:
This may also be written more generally as using the gauge-covariant derivative , because the commutator . With and Coulomb constant , the classical Maxwell equation for electric charge strength is:
which spacetime-covariantly includes Gauss’ electricity and Ampere’s current laws. The classical equation for magnetic charge strength is
which spacetime-covariantly includes Gauss’ magnetism and Faraday’s induction laws. The zero in the monopole equation and thus the non-existence of magnetic monopoles (setting aside possible Dirac charge quantization) arises from the flat spacetime commutator of ordinary derivatives being . In integral form, the Gauss’ magnetism law component of the above becomes , whereby there is no net flux of magnetic fields across closed spatial surfaces. (Note: The point of various “bag models†of QCD quark confinement, is that there is similarly no net flux of color charge across the closed spatial surfaces of color-neutral baryons.)
Summing the four-gradient with the above electric charge strength, we readily obtain:
which is the continuity equation governing the conservation of electric charge. This becomes zero, once again, because of flat spacetime commutator .
In quantum electrodynamics, the charge density becomes related to the Dirac wavefunctions for individual fermions by where is the electric charge strength related to the running "fine structure" coupling by , and for the electron, up and down fermions, and their higher-generational counterparts. Meanwhile the propagators for the individual photons which form the gauge fields are obtained by inverting the electric charge equation and converting from configuration into momentum space using the substitution and the prescription. Because the charge equation is not invertible without taking some further steps, it is customary to utilize the gauge condition to obtain
which includes the photon propagator up to a factor of . Alternatively, one can introduce a Proca mass by hand into the charge equation. Then, is no longer a gauge condition but a requirement to maintain continuity (charge conservation), and with we arrive at the inverse:
which includes a massive vector boson propagator up to . Of course, adding a mass by hand destroys renormalizability, so it is necessary to find a way that this can be restored.
In Yang-Mills Gauge Theory, becomes a non-commuting gauge field, , and the field strength therefore graduates to the gauge-covariant, not gauge-invariant:
With A replaced by G, it will be seen that this contains the equation from the Mathematical overview above. Using differential forms, this may be written as the curvature arising from the gauge connection, see [1] at pages 1 and 2. The non-linearity of Yang-Mills gauge theories becomes apparent if one uses the above to advance the source-free Lagrangian from the Mathematical overview to:
which includes three- and four-gauge boson interaction vertices.
Yang-Mills gauge theory differs from the abelian gauge theory of U(1) electrodynamics, by the mathematical and physical consequences of what happens when the gauge fields go from commuting to non-commuting in this way. PatentPhysicist ( talk) 17:34, 21 February 2021 (UTC)
PS: I noticed that this is a level 5 vital priority article, but only B class rated. I have studied Yang-Mill gauge theories for over 15 years, and would like to try to contribute to raising this. PatentPhysicist ( talk) 02:51, 22 February 2021 (UTC)
I just added the section as written above, to the main article. PatentPhysicist ( talk) 18:54, 23 February 2021 (UTC)
References
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
Ok, I'm going to get the ball rolling by pointing out that there is pretty much no information here. Unfortunately, I don't know enough about Yang-Mills theories to contribute, so I think we really need an expert. StewartMH ( talk) 20:54, 18 April 2008 (UTC)
This voice should be renamed from "Yang-Mills" to "Yang-Mills theory". Pra1998 ( talk) 10:55, 24 November 2008 (UTC)
I have prepared a jpeg file with latex containing Feynman's rules for Yang-Mills theory. I would like to insert this image into this article as it is in need of it. Please, could you help me? Thanks beforehand. Pra1998 ( talk) 11:21, 25 November 2008 (UTC)
I think that any encyclopedia must have an article about Yang-Mills theory. The reason is that Yang-Mills theories describe strong and electro-weak interactions and when these are discussed one is forced to recall them anyway.
About the quality of the article, I am not fully convinced that the B class is the right one. But it is no more at a starting level and I have substantially put forward a well developed scheme to build upon. The aim is to reach a higher level of quality making this article useful both to students and researchers. Of course, any suggestion about is welcome. Pra1998 ( talk) 16:31, 2 December 2008 (UTC)
Yang-Mills theory represents a great mathematical challenge and so also wikipedia should consider as such entering into the WikiProject Mathematics. Pra1998 ( talk) 16:34, 2 December 2008 (UTC)
I take this chance to thank Michael for his intervention. Section about integrable solutions gives no other than an a class of exact classical solutions of Yang-Mills equations and this is always true independently on any theoretical construction one can ever do. -- Pra1998 ( talk) 10:24, 25 February 2009 (UTC)
As you may know, Peter Woit is a critic of science. By "critic of science" one means the same as a movie critic that does not produce any original work by his own but is very active in criticizing other work. This section contains no other than a class of exact solutions of classical Yang-Mills equation and this is plain mathematics without further claim. I could have as well cited the Smilga's book that proposed such solutions and the result would be the same.
The right approach here would be eventually to remove any claim about Frasca's work maintaining the exact solutions of Yang-Mills equations that are true independently on Woit point of view.
Addendum: There is currently, in our community, the idea that an ignored idea is a wrong idea. Of course, this is plainly false as history of physics taught us. Rather, fashions make the path and new ideas may find serious difficulties to affirm. What is really important is that there exist a lot of ideas that are published in physics journals everyday. It is this that makes our field really sane.-- Pra1998 ( talk) 09:21, 26 February 2009 (UTC)
-- Pra1998 ( talk) 08:15, 26 February 2009 (UTC)
Headbomb, sorry for the improper comment and thank you for pointing me this out. I apologize if my sentence implied an offense. I think you hit the point and this was the argument I was making. This is just a class of exact solutions for classical Yang-Mills equations and I think they should be there as also other ones that should be inserted. Of course, there is no harm if this implies removing Frasca ref. and pointing just to Smilga's one.-- Pra1998 ( talk) 10:14, 26 February 2009 (UTC)
If, by "critic of science", you mean well-respected contributor of science, then yes. The characterisation of Peter Woit as a mere "critic of science" is akin to to calling Stanley Kubrick a "film critic." -- Logoskakou ( talk) 15:49, 26 February 2009 (UTC)
On a general note, I'm beginning to wonder if I'm not smelling some WP:MEAT here. A newly registered editor removes material, then an editor inactive for one year replies and heralds the first one as being "really super". Nothing to warrant ignoring WP:AGF at this point, but there's some red flags being raised. Headbomb { ταλκ κοντÏιβς – WP Physics} 16:42, 26 February 2009 (UTC)
The last part of this article has nothing to do with conventional main-stream understanding of Yang-Mills theory. It is purely the work of Marco Frasca, a physicist who appears to have no institutional affiliation (his papers carry his home address) who I suspect is "Pra1998". There is no reference arguing against these ideas since they are completely ignored by the main-stream. This sort of thing should have no place here. Frasca is free to argue for his ideas on his blog, but he shouldn't be doing it by inserting them into Wikipedia entries. —Preceding unsigned comment added by Peterwoit ( talk • contribs) 01:38, 26 February 2009 (UTC)
I don't know much about Wikipedia standards. The bottom line is that the content in question is unconventional speculation due to Frasca, speculation that I don't think anyone else is much interested in or convinced by. Lots of such ideas are published in journals, and then mostly ignored. Personally I don't think they belong on Wikipedia at all, but they certainly don't belong in an entry like this on one of the core ideas of modern physics. Peterwoit ( talk) 01:54, 26 February 2009 (UTC)
I read the section in some details, and while I don't understand one thing about it, it does feels like WP:OR. Especially with sentences like "the infrared theory has been recently formulated" and "the results appear to be in agreement with computations with lattice field theory". I don't know how recent 2006 is in QFT, but this may be too immature to include in WP. Headbomb { ταλκ κοντÏιβς – WP Physics} 17:17, 26 February 2009 (UTC)
I've reverted to the pre-revert war state of the article. Beware of revert wars, as you may be blocked for it. Now that being said (I'm no admin, I'm just warning people that you could very well get banned for this), it is a bit sad that Mr. Woit simply did not explain his position in more details and gave up on the whole thing rather than explain to us how the Frasca/Smigma articles/books are not reliable when it comes to this topic ( see his blog). Anyway, I left a message on his talk page, perhaps he'll come back an explain where Frasca got it wrong and give us some refs. Headbomb { ταλκ κοντÏιβς – WP Physics} 16:57, 26 February 2009 (UTC)
Thanks AJ, couldn't have said it better myself. Peterwoit ( talk) 20:00, 26 February 2009 (UTC)
Dear Headbomb,
Thank you very much for your intervention. People here do not even know how Wikipedia works. -- Pra1998 ( talk) 18:30, 26 February 2009 (UTC)
The pre revert war is the one with Marco Frasca version, so I reverted to that version because otherwise people will NOT be able to judge the material properly. They will have to click on the history of the article, which is already extremely confusing. The dispute warning is enough to make sure one thinks that the information presented can be accurate or not, and is wainting for an evaluation on the talk page. If anyones think it's necessary, move the section for apreciation on the talk page, but please, do not delete it from the main article. Daniel de França ( talk) 12:34, 27 February 2009 (UTC)
The first introductory paragraph implies that the U(1) of SU(2)xU(1) on electroweak theory is the U(1) of QED. This is not the case -the U(1) in electroweak is u(1) hypercharge. —Preceding unsigned comment added by 128.230.72.196 ( talk) 17:04, 12 March 2009 (UTC)
Per the arguments presented by everyone here, consensus is that this is original research, non-notable, and potentially self-publication, I have deleted this section. Headbomb { ταλκ κοντÏιβς – WP Physics} 00:14, 27 February 2009 (UTC)
See also Wikipedia:Suggestions for COI compliance. Headbomb { ταλκ κοντÏιβς – WP Physics} 01:01, 27 February 2009 (UTC)
Headbomb, do you think science is something decided by majority? Before an overwhelming number of people complaining, without a real understanding of the content, you removed it. The point here is that I am not a person who wrote a libel against a part of the scientific community becoming an instantaneous star, with anyhow a poor scientific curriculum, able to move a lot of people against a single one. If this is a serious project you were not.—Preceding unsigned comment added by Pra1998 ( talk • contribs) 13:20, 27 February 2009 (UTC)
It may be relevant to point out that one of the references cited in the disputed section [3] has a significant error in it, despite being published. Namely, in the proof of Theorem 1, the author is assuming that an extremum A for the Yang-Mills action for a special class of connections (namely those in which and all other components vanish) is necessarily an extremum for the Yang-Mills action for all other connections also, but this is not the case (just because , for instance, for A' of this special form, does not imply that for general A'). Since one needs to be an extremiser (or critical point) in the space of all connections in order to be a solution to the Yang-Mills equations, the mapping provided in Theorem 1 has not been shown to actually produce solutions to the Yang-Mills equation (and I suspect that if one actually checks the Yang-Mills equation for this mapping, that one will not in fact get such a solution). Terry ( talk) 20:32, 28 February 2009 (UTC)
Terry, the author assumes that exists a class of solutions that maps Yang-Mills action on the one of a scalar field. You can find that above solution is indeed a solution of Yang-Mills equations. Check Smilga book [4]. Instead to rely on questionable theoretical arguments, take Maple or Mathematica and check it. There is no claim about what you are saying -- Pra1998 ( talk) 11:27, 2 March 2009 (UTC)
Dear Headbomb, you can find good reviews of some Frasca's works here [6], e.g. this MR2345223 (2008f:81084) and this MR2332380 (2008e:81089). If you belong to some recognized institution you should have access to this mathematical database. But here I just entered into this discussion area to answer a wrong affirmation by Terry, a claim that can be easily proved wrong with Maple or Mathematica. I have no interest to defend Frasca's work as you can see from my preceding interventions where I would have removed the refs without problem. The fact that you removed also Smilga's book, well, that is your choice. You removed just plain mathematics but it is your own right.Thank you anyway.-- Pra1998 ( talk) 20:31, 2 March 2009 (UTC)
Headbomb, I give you the exact refs. to look for. If you are not able to cope with scientific databases please ask somebody expert. This is not google, this is a database of American Mathematical Society, well known to people doing research, that gives reviews of papers after publication. Please, ask to a person being an active researcher in a recognized institution.-- Pra1998 ( talk) 07:56, 3 March 2009 (UTC)
I have added some references but DOI numbers do not appear even if they seem correctly inserted. Any help?-- Pra1998 ( talk) 13:34, 5 May 2010 (UTC)
A user from wanadoo.fr added a disputable comment having no value for Wikipedia. I removed as vandalism. This is again the question if new physics results should go on Wikipedia producing such kind of effects. Let me know your view. But adding such a comment in the article rather than the discussion is pure vandalism.-- Pra1998 ( talk) 16:18, 6 November 2010 (UTC)
An anonymous user introduced this:
"Prior to Yang-Mill's publication, Pauli had given a seminar on the same idea but did not publish because he did not believe it would work at the time. When Yang gave his talk, Pauli asked Yang a question which Yang could not answer. Yang's talk ended abruptly. Yang then avoided Pauli even though Pauli tried to reach Yang to discuss the idea in more detail. Yang's behavior led many scientists to question how much Yang had to do with the origination of the idea."
I think this kind of stories should be well supported by proper citations. Does anyone out there know this? —Preceding unsigned comment added by Pra1998 ( talk • contribs) 08:43, 24 November 2009 (UTC)
Michael, sorry for omitting my signature. Just oversight. I tried to use citation needed but it did not seem to work in preview and so I have chosen the bad way.-- Pra1998 ( talk) 16:49, 24 November 2009 (UTC)
't Hooft asked Yang to provide some materials for how he and Mills developed Yang Mills theory. All Yang was able to provide for 't Hooft's " 50 years of Yang Mills theory" were a couple pages from his graduate student days...does that dovetail with above discussion that Yang had actually borrowed Pauli's unpublished idea and got away with it since nobody at that time thought Yang mills was anything significant?
Also, Yang co-published a paper shortly after his Yang Mills with T.D. Lee, where the key argument was anti (against) Yang Mills thoery. So, Yang himself was not convinced about the validity of Yang Mills theory at that time. —Preceding unsigned comment added by 163.166.135.44 ( talk) 01:27, 24 December 2009 (UTC)
There are documents which show that wolfgang Pauli developed in 1953 the first consistent generalization of the five-dimensional theory of Kaluza, Klein, Fock and others to a higher dimensional internal space. Because Pauli saw no way to give masses to the gauge bosons, he refrained from publishing his results formally. Pauli gave talks on the subject and many physicists of the time, including Yang, debated Pauli's unplublished theory.(See "On Pauli's invention of non-abrlian Kaluza-Klein Theory in 1953") —Preceding unsigned comment added by 69.156.210.199 ( talk) 13:50, 27 October 2010 (UTC)
About Pauli in 1953: apparently he compactified a 6-dimensional space and found SU(2) gauge theory (much like Kaluza and Klein toroidally compactified a 5-dimensional space and found U(1) gauge theory). However, Yang and Mills showed how requiring local gauge invariance severely restricts the terms in the Lagrangian. To me, these are very different things: on the one hand Pauli found one SU(2) gauge theory, and on the other hand Yang and Mills showed that it's basically the only reasonable one out there. We can debate forever from where Yang and Mills got their idea, but to me it's clear that the point here is the importance of local gauge invariance, and this is the point Yang and Mills made. —Preceding unsigned comment added by 132.206.126.18 ( talk) 21:24, 15 February 2011 (UTC)
I'm a complete layman in the field, but IMO a lot of formulas are bloated and could be written more concisely in a coordinate-free manner and/or with some intermediate definitions. — Kallikanzarid talk 18:47, 19 February 2011 (UTC)
The lack of any citations in the Mathematical Overview section of the article seems like a bit of a problem; in particular it makes it almost impossible to use the article as a starting point for a review of the mathematics of Yang-Mills theory (as I currently am).
In particular, I'm looking for a citation for Pra1998's edit in 2009 adding the note about the lack of distinction between and upper and lower a indices; this fact seems to be taken implicitly in all books and articles I've found so far and was hoping someone would know a specific source explicitly stating that it is legitimate.
I've also made a post at the reference desk because, being new, I wasn't sure what the best channel was.
https://en.wikipedia.org/?title=Wikipedia:Reference_desk/Science&oldid=648352928#Citation_for_Yang-Mills_Theory_-_Mathematical_Overview — Preceding unsigned comment added by Tjlr2 ( talk • contribs) 18:09, 22 February 2015 (UTC)
Is Yang-Mills theory science or math? They are not the same thing.
The lead says, "Yang–Mills theory seeks to describe the behavior of elementary particles..." which suggests that its developers have intended to provide a mathematical model for this aspect of the physical world - that is, they intend to provide a tool for elucidating a scientific theory of the world.
After providing a précis list of the symmetry groups of the Standard Model, in the 'History and theoretical description' section I read "This may be the reason why confinement has not been theoretically proven, though it is a consistent experimental observation." While as a lay person, I understand that confinement is in fact what has been observed, I don't at all understand what - in the context of a scientific theory of the world - can even be meant by "theoretically proven".
I know that it is common to refer to large parts of mathematics as the 'theory' of this or that, as the Theory of Numbers' and so forth and though I think this is not nonsensical, I am uncomfortable with this sort of construction appearing here, if, as in the lead, 'YM Theory' is intended to be an article describing a scientific theory of the natural world. Theorems are objects of mathematics. Theories - which are always contingent and so are unprovable - are objects of science.
In 1979, during his noted series of popular lectures given at the University of Aukland, New Zealand, Richard Feynman said
How is Feynman's discussion of the EM coupling constant not an example of the inappropriateness of imagining that proving a mathematical theorem or proving the consistency of some assertions in a symbolic calculus is the same thing as 'proving' an assertion about the world? Have I not argued sufficiently for the affinity between on the one hand claims for mathematical (geometric, topological etc.) derivations of α and on the other hand, hope for 'mathematical proof' that confinement is necessary?
Alternately, I understand that this observation is supported by a thirty-five-year-old perspective from a man with a complicated attitude toward 'villozovy' and so on. Is Feynman's view now considered dowdy? Or still just inconvenient? Rt3368 ( talk) 17:03, 25 August 2015 (UTC)
At this date (6/11/2017), it's written "{\displaystyle [A]=[L^{\frac {2-D}{2}}]} [A]=[L^{\frac {2-D}{2}}]" . I think it's 2-\frac{D}{2}, but I could be wrong (my own computation gives this power, and I also think it agrees with the next result, contrary to the given power) — Preceding unsigned comment added by 134.157.64.191 ( talk) 18:23, 6 November 2017 (UTC)
I think that, in agreement with Woit's ideas we should remove all the section. The paper he is questioning is regularly published in a prestigious journal and is a collaboration with a reputable physicist.-- Pra1998 ( talk) 21:52, 27 April 2018 (UTC)
Could we please discuss the passages and parts regarding known or unknown quantities which seem to inflame our anonymous editor so much? I'm afraid I don't know much about theoretical physics, but I'm willing to try to learn. —
Javert2113 (
talk)
15:05, 29 April 2018 (UTC)
There is no need to deal with the complex scientific issues here. Pra1998=Marco Frasca, and my understanding is that Wikipedia policy does not allow people to add references to their own work to Wikipedia pages. Peterwoit ( talk) 14:50, 30 April 2018 (UTC)
I would like to add a new section to this article, with the above section title, following the section "Quantization." My proposed section is below. Are there any objections or suggestions, prior to my doing so?
Studying the physics of Yang-Mills gauge theory requires understanding what happens to Maxwell’s electrodynamics, and U(1) quantum electrodynamics (QED), when Maxwell’s commuting (abelian) gauge fields become non-commuting (nonabelian) gauge fields covariantly transforming, for example, under the compact simple Yang-Mills gauge group SU(N) with NxN Hermitian generators and a commutator typically normalized such that for each . Whereas electrodynamics is a linear theory in which the gauge fields to not interact with one another, Yang-Mills theory is highly nonlinear with mutual interactions amongst the gauge fields.
In flat spacetime, in classical electrodynamics, a gauge-invariant field strength is related to the gauge fields by:
This may also be written more generally as using the gauge-covariant derivative , because the commutator . With and Coulomb constant , the classical Maxwell equation for electric charge strength is:
which spacetime-covariantly includes Gauss’ electricity and Ampere’s current laws. The classical equation for magnetic charge strength is
which spacetime-covariantly includes Gauss’ magnetism and Faraday’s induction laws. The zero in the monopole equation and thus the non-existence of magnetic monopoles (setting aside possible Dirac charge quantization) arises from the flat spacetime commutator of ordinary derivatives being . In integral form, the Gauss’ magnetism law component of the above becomes , whereby there is no net flux of magnetic fields across closed spatial surfaces. (Note: The point of various “bag models†of QCD quark confinement, is that there is similarly no net flux of color charge across the closed spatial surfaces of color-neutral baryons.)
Summing the four-gradient with the above electric charge strength, we readily obtain:
which is the continuity equation governing the conservation of electric charge. This becomes zero, once again, because of flat spacetime commutator .
In quantum electrodynamics, the charge density becomes related to the Dirac wavefunctions for individual fermions by where is the electric charge strength related to the running "fine structure" coupling by , and for the electron, up and down fermions, and their higher-generational counterparts. Meanwhile the propagators for the individual photons which form the gauge fields are obtained by inverting the electric charge equation and converting from configuration into momentum space using the substitution and the prescription. Because the charge equation is not invertible without taking some further steps, it is customary to utilize the gauge condition to obtain
which includes the photon propagator up to a factor of . Alternatively, one can introduce a Proca mass by hand into the charge equation. Then, is no longer a gauge condition but a requirement to maintain continuity (charge conservation), and with we arrive at the inverse:
which includes a massive vector boson propagator up to . Of course, adding a mass by hand destroys renormalizability, so it is necessary to find a way that this can be restored.
In Yang-Mills Gauge Theory, becomes a non-commuting gauge field, , and the field strength therefore graduates to the gauge-covariant, not gauge-invariant:
With A replaced by G, it will be seen that this contains the equation from the Mathematical overview above. Using differential forms, this may be written as the curvature arising from the gauge connection, see [1] at pages 1 and 2. The non-linearity of Yang-Mills gauge theories becomes apparent if one uses the above to advance the source-free Lagrangian from the Mathematical overview to:
which includes three- and four-gauge boson interaction vertices.
Yang-Mills gauge theory differs from the abelian gauge theory of U(1) electrodynamics, by the mathematical and physical consequences of what happens when the gauge fields go from commuting to non-commuting in this way. PatentPhysicist ( talk) 17:34, 21 February 2021 (UTC)
PS: I noticed that this is a level 5 vital priority article, but only B class rated. I have studied Yang-Mill gauge theories for over 15 years, and would like to try to contribute to raising this. PatentPhysicist ( talk) 02:51, 22 February 2021 (UTC)
I just added the section as written above, to the main article. PatentPhysicist ( talk) 18:54, 23 February 2021 (UTC)
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