Talk:Yang–Mills theory

Total lack of information

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)

Not a *total* lack of information. I thought some info is better than none! --Michael C. Price ^talk 22:15, 18 April 2008 (UTC)

Renaming

This voice should be renamed from "Yang-Mills" to "Yang-Mills theory". Pra1998 (talk) 10:55, 24 November 2008 (UTC)

Yeah, I've made the request to move it.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 11:35, 24 November 2008 (UTC)

And now it's moved.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 17:39, 24 November 2008 (UTC)

Image of Feynman's rules

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'm not very familiar with uploading images, but User:Mike Peel said he could help with things like that.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 21:16, 25 November 2008 (UTC)

Rating

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)

Mathematical rating

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)

Presumed speculative ideas

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)

Marco Frasca

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)

What about if we hived off the material into its own article? It has been published in a RS, after all. --Michael C. Price ^talk 01:41, 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 know you think they certainly don't belong in an entry like this on one of the core ideas of modern physics -- that's why I'm asking you if it should be hived off into a separate article.--Michael C. Price ^talk 02:15, 26 February 2009 (UTC)

No. If nothing else, the information that is posted by Pra1998 would fall under "original research", though I think it is generous to call it research. As per Wikipedia's policy on original research, it should neither be in this article nor hived in to its own article. --Logoskakou (talk) 15:49, 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_{κοντριβς} – WP Physics} 17:17, 26 February 2009 (UTC)

The material may or may not be original research, but it's not an appropriate topic for the main article on Yang-Mills theory. The material itself is rather specialized. Moreover, the relation between the material and the main concerns of Yang-Mills theory is speculative, which goes a long way towards explaining why it's so poorly integrated with the rest of the article. I would recommend hiving it off or deleting it entirely, and I'm not sure that I would recommend including a link to the new article in the main Yang-Mills article. (Full disclosure: I'm a math PhD student. I work on topics related to Yang-Mills theory. I found out about this issue via Woit's blog, and thought that since I know something abou the topic, I ought to speak up.) --A.J. Tolland —Preceding unsigned comment added by 198.129.67.74 (talk) 19:05, 26 February 2009 (UTC)

I also have read the section in some detail and would note that it also feels like original research. As a regular consumer of the Wiki information on math and physics I would prefer not to have to try to discern what is OR and what is not, particularly in an article as important as this one. That fact that Pra1998 is the author of this OR makes me even more skeptical that this information should remain. The references other than the OR itself (i.e. ref. 5 and 6) is Smilga's book on QCD but when one looks in that source the support for the information in this part of the article is non-existent. One can see from Frasca's blog where he is referencing a single aside comment from Smilga's book. See: http://marcofrasca.wordpress.com/2008/10/25/smilgas-choice-and-the-mapping-theorem/ Looking in the book one can find the referenced statement (page 13) which reads: "The solution (1.32) is a non-linear standing wave. By a Lorentz boost, one can obtain as well solutions describing nonlinear propagating waves. These solutions so not seem to have a particular physical significance, but maybe their meaning has not yet been unravelled." See: http://books.google.com/books?id=qkkYFaat_ZgC&pg=PR8&lpg=PR8&dq=Smilga+qft&source=bl&ots=DNd34MV2zG&sig=_blV-CZgAN_412g8IX3aIAGxf6o&hl=en&ei=Ht-mSe6TC8PQkAW8v83dDQ&sa=X&oi=book_result&resnum=1&ct=result#PPA13,M1 for the context. It is clear that Frasca's work and this section of the article are related to studying these solutions but it is also clear that his work is at this point speculative in nature and does not belong in this article. On a related idea, the so-called Smilga's Choice appears to be a term invented by Frasca, if you leave the article in or hive it then maybe he or you could find us a reference to this. OK, this is my first comment on wiki, I hope I did this correctly. Mbkmbk9 (talk) 19:48, 26 February 2009 (UTC)

Peter Woit

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)

I don't know anything about anything here, but I wonder how you can characterize Peter Woit as some armchair critic of science (see WP:NPA btw). Perhaps the debate here is equivalent to debating whether or not complex exponentials are solutions to second order differential equations, in which case I would agree that the criticism has no ground to stand on. Regardless, the sources for including these solutions seem to be reliable (Smilga's book has generally positive reviews, including a recommendation from Mathematical Reviews, with the negative reviews focusing on the mathematical complexity and lack of efforts made to make it more accessible), independent of each other (i.e. not from two coworkers), and not made by people known to be crackheads. It would take more than simply saying "it's not because it's published that people are paying attention to it" to convince me that this should not be included. If this cannot be resolved, I suggest asking for feedback at WP:PHYS. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 09:56, 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)

Not to insult Peterwoit here, but he only made 5 (contested) edits in two days. That's hardly a Stanly Kubrick worthy comparison.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 16:42, 26 February 2009 (UTC)

Ah, you're referring to this, not his wikipedia edits. My bad.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 16:48, 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_{κοντριβς} – WP Physics} 16:42, 26 February 2009 (UTC)

Please see Peter Woit's blog (at [1]), I don't think you need to be quite so suspicious (at least not in this case). In any case, Peter Woit is not the issue here, what he's pointing out is quite valid.--Innerproduct (talk) 18:22, 26 February 2009 (UTC)

WP:3RR warning

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_{κοντριβς} – WP Physics} 16:57, 26 February 2009 (UTC)

I'm not Peter, but I can give it a shot. The problem is not that the Smilga book is unreliable. The problem is that the material in the new section isn't sufficiently notable to be included in the main article on Yang-Mills theory. Yang-Mills is a large subject, and the main article can't reasonably cover every conceivable topic. The solutions from Smilga's book are solutions to the Yang-Mills equations, but they are not solutions that everyone who works with Yang-Mills theory needs to know about. (Most books on Yang-Mills don't mention these solutions.) The situation is further complicated because these solutions are presented in the context of some highly speculative research by Frasca (Pra1998), who authored the section. I would recommend deleting the section, as there's probably not enough notable material here to justify the effort required to extract it from the speculation and original research. --A.J. Tolland —Preceding unsigned comment added by 198.129.67.74 (talk) 19:51, 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)

I don't really understand why Headbomb chose to intervene at all. As you admit yourself, this is not an area of your expertise.--Innerproduct (talk) 18:34, 26 February 2009 (UTC)

Regardless of who's right in this dispute, revert-warring without discussion is not the way to solve it. Headbomb quite properly restored The Wrong Version, and if further reverts happen without discussion here then page protection might be warranted. It seems to me that maybe the appropriate way to resolve this would be to set up a request for comment — someone who does know something about this subject want to set one up? —David Eppstein (talk) 19:36, 26 February 2009 (UTC)

I've restored to the previous version because there was a revert war, not because I supported it. Upon further review, there is definitely a conflict of interest here, or at the very least, enough grounds to suspect one as well as concerns of accuracy and original research (hence the tags on the article, were there concerns of conflict of interest and original research, only the disputed tag would've made its way). The physics project was notified, and apparently a tons of people came here from Peter Woit's blog. Everyone seems to agree that this section is at best non-notable, and at worse self-publishing. So the section should be removed from the article. Whether these people are aware of how wikipedia works or not is irrelevant, consensus is that should be removed. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 00:03, 27 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)

Integrable solutions of classical Yang-Mills equations and QFT (Disputed section)

Disputed section

One of the main difficulties that one meets on managing Yang-Mills theory at low energies is that Hamiltonian homogeneous equations of the theory admit essentially chaotic solutions and nobody is able to formulate a quantum field theory starting from such solutions. But, beside chaotic solutions, this theory also admits integrable solutions that can be used for these aims. These solutions can be found with the so called Smilga's choice that permits to fully map Yang-Mills theory on a $\lambda \phi ^{4}$ massless field theory and, for this case, the infrared theory has been recently formulated . So, one can compute the propagator and the spectrum . The results appear to be in agreement with computations with lattice field theory yielding a zero momentum propagator

$\ \Delta (\omega )=\sum _{n=0}^{\infty }{\frac {B_{n}}{\omega ^{2}-\omega _{n}^{2}+i\epsilon }}$

being

$\ B_{n}=(2n+1){\frac {\pi ^{2}}{K^{2}(i)}}{\frac {(-1)^{n+1}e^{-(n+{\frac {1}{2}})\pi }}{1+e^{-(2n+1)\pi }}}$,

and a mass spectrum

$\ \omega _{n}=\left(n+{\frac {1}{2}}\right){\frac {\pi }{K(i)}}\left({\frac {Ng^{2}}{2}}\right)^{\frac {1}{4}}\Lambda$

proper to an harmonic oscillator. The ghost field has the same propagator as a free particle, i.e. it decouples from the gluon field.

An example of such classical solutions can be yielded for SU(2) gauge group (but it is also easy to obtain it for SU(3))

$\ A_{\mu }^{a}=\eta _{\mu }^{a}\Lambda \left({\frac {1}{g^{1 \over 2}}}\right){\rm {sn}}(p\cdot x+\phi ,i)$

being a Jacobi elliptic function, $\Lambda$ and $\phi$ integration constants and $\eta _{\mu }^{a}=((0,1,0,0),(0,0,1,0),(0,0,0,1))$. This solution for Yang-Mills equations holds only if the following dispersion relation holds

$\ p^{2}=g\Lambda ^{2}$

showing in this way as a massless theory can have classical massive solutions.

Computation of the gluon propagator is essential because it permits to obtain, starting from quantum chromodynamics, a Nambu-Jona-Lasinio model and all hadronic phenomenology seen at lower energies can be derived. Research in this field is currently very active and important results are expected shortly.

Removed "Integrable solutions of classical Yang-Mills equations and QFT"

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_{κοντριβς} – WP Physics} 00:14, 27 February 2009 (UTC)

See also Wikipedia:Suggestions for COI compliance.Headbomb {^ταλκ_{κοντριβς} – 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)

Pra1998, you would do well to read the Wikipedia guidelines on original research, notability, and conflict of interest, as Headbomb has already mentioned. There is no vendetta against you. Read and you will understand. - mako 00:57, 28 February 2009 (UTC)

The material you want to include is from 2006–2008, and so this material didn't have very much time to mature. There is strong opposition to including this in the YM article, for concerns of conflicts of interest, original research, non-notability. My personal opinion here is irrelevant, consensus is that this should not be included. If this is really notable, then you'll be able to find a review which cites Frasca's work positively which you may or may not be (although the evidence is pretty strong that you are indeed Frasca). Science is not decided by majority, true, but it also is not decided by lone rogues who do uses public forums of discussion to push their theories. Find a review which cites Frasca's work positively, and then it can be used in here. Otherwise, the consensus probably won't change that this is not worthy of inclusion. I'm not saying that Frasca's work is crap, or crank science or anything like that, I'm just saying that its place is not on Wokipedia. Note that most of your contribution to this article is deemed very acceptable (aka this part [2])

As far as libel, you may not have written one to become a "scientific star", but you certainly have no problem depicting Woit's curriculum as "being poor". If you have a problem with this material being removed, either find us a review citing Frasca positively, or take it to WP:RfC. See also Wikipedia:Suggestions for COI complianceHeadbomb {^ταλκ_{κοντριβς} – WP Physics} 01:00, 28 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 $A_{1}^{1}=A_{2}^{2}=A_{3}^{3}$ 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 $YM(A)\geq YM(A')$, for instance, for A' of this special form, does not imply that $YM(A)\geq YM(A')$ 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)

Pra1998, I think you may be confusing the Yang-Mills action ${\frac {1}{4}}\int {\hbox{tr}}(F^{\mu \nu }F_{\mu \nu })$ with the Yang-Mills equations $D^{\mu }F_{\mu \nu }^{a}=0$. If one takes the ansatz $A_{1}^{1}=A_{2}^{2}=A_{3}^{3}=\phi$ suggested in the paper, with all other components zero, with $\phi$ obeying the $\phi ^{3}$ equation, then the Yang-Mills equations $D^{\mu }F_{\mu \nu }^{a}=0$ do not hold. For instance, the a=1, $\nu =2$ component of $D^{\mu }F_{\mu \nu }^{a}$ has a top order term of $\partial _{1}\partial _{2}\phi$ plus lower order terms, and this does not vanish for general solutions of the equation $\partial ^{\mu }\partial _{\mu }\phi =\phi ^{3}$.

I don't think Smilga's book makes the claim that every solution of the $\phi ^{3}$ equation maps to a solution to the Yang-Mills equation, as this paper does, but I would be interested to see a specific page number reference if I am mistaken. Terry (talk) 00:31, 3 March 2009 (UTC)

"Do it yourself" isn't much of an argument here. If you have reviews or books giving positive ratings about the accuracy/soundness/pertinence of Frasca's work, then provide those, otherwise you're have nothing to stand on. If you can't find those, then this does not meet WP:NOTABILITY, regardless of whether or not the material is correct. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 13:31, 2 March 2009 (UTC)

Dear Headbomb, you can find good reviews of some Frasca's works here [5], 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)

That's a search engine. That's the equivalent of saying "if don't believe me, you can find good source here [6]". I'm not about to wade through possibly hundreds of hits (and even if it were ten hits), reading 50-100 pages documents looking for one which cites Frasca favourably. Headbomb {^ταλκ_{κοντριβς} – WP Physics} 00:06, 3 March 2009 (UTC)