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IIRC goldstone bosons occur when there is any spontaneously broken global symmetry(other than supersymmetry in which case there is a fermion called a goldstino)
JeffBobFrank 03:30, 4 May 2004 (UTC)[reply]
I think is a bit confusing the explanation of the explicitly breaking of the symmetry. It should remark that if the explicitly breaking is small, then there also exist (pseudo-)Goldstone bosons which acquire a little mass, due to the small explicitly breaking, but their mass is very small compared to the mass of the other particles in the model, so they are still the lightest degrees of freedom.Villatortilla 02:46, 1 February 2007 (UTC).[reply]
I see a contradiction between the following three statements:
An example of a Goldstone boson is the Higgs boson in the Standard Model. (on this page)
In general the Goldstone boson is always massless (on this page)
The Higgs boson itself has mass. As of 2004, the best estimate for the mass is 117 GeV, and the theoretical upper limit is 251 GeV. (on the Higgs boson page)
I suspect the second statement of being incorrect, but I'm no physicist. MatthewWilcox 17:39, 15 Dec 2004 (UTC)
The first statement is incorrect. The (nonexistent) Goldstone boson has been gauged away. Some physicists like to say "eaten up", but that's misleading. Phys 19:02, 17 Dec 2004 (UTC)
The first statement is incorrect: The Higgs is the only member of the Higgs complex doublet, so the only one of these four excitations, which is not a goldston (usually). The other three excitations would have been goldstons, had they not been gauged/eaten away by the respective gauge bosons, Ws, and Z, in the so-called Higgs mechanism. Higgs' name is better attached to the vanished goldstons, than to the non-goldston remnant, by now universally called "the Higgs". This remnant is the heaviest survivor of the broken multiplet, a reduced nonlinear realization array now, rather than a multiplet, and is analogous to the sgoldstino of the broken supermultiplets outlined in the article, or the legendary σ of the σ-model, the pions being the pseudogoldstons. Cuzkatzimhut (talk) 19:24, 18 June 2009 (UTC)[reply]
Usually people say "Goldstone boson" rather than "Nambu-Goldstone boson". It is also supported by Google:
"Nambu-Goldstone boson" 20k hits
"Goldstone boson" 136k hits
Therefore, I'd suggest renaming the article to "Goldstone boson", and mentioning "Nambu-Goldstone boson" as an alternative name. Yevgeny Kats 05:14, 24 July 2006 (UTC)[reply]
Names are names, and reflect a confused political reality. Nambu did get his Nobel prize for introducing/discovering these bosons among others, in 2008. In the same ironic vein, Higgs, of course, was not the first to introduce Higgs bosons, in particle physics, either – François Englert and Robert Brout were. Enforcing Google-count realities merely validates the stampede. The published record, however,
controls, in the end. The reader may benefit from simply looking at the papers, now cited. Cuzkatzimhut (talk) 01:03, 18 June 2009 (UTC)[reply]
Does anyone have a graphic of the "mexican hat" potential for the example given in the section titled "A Simple Example"? It would make for a clearer discussion, especially the bit at the end where the Goldstone field is described as parameterizing the "curve of possible vacuum states". HEL 02:03, 5 November 2006 (UTC)[reply]
Someone else (not me) has already uploaded the image . Maliz 19:49, 5 November 2006 (UTC)[reply]
Can somebody plot it in polar coordinates, so that ugly corner spikes go away?Likebox (talk) 21:00, 4 November 2008 (UTC)[reply]
How's this? I made it today. Perhaps a labelled z axis would make it a better illustration? RupertMillard (Talk) 15:43, 11 September 2009 (UTC)[reply]
Looks nice; labeling axes can only confuse, not clarify the paradigm. Cuzkatzimhut (talk) —Preceding undated comment added 16:25, 11 September 2009 (UTC).[reply]
Could someone in the know actually state Goldstone's theorem in the "Goldstone's theorem" section? The section discusses it but doesn't seem to state what the theorem actually is. --Doradus (talk) 19:03, 29 December 2010 (UTC)[reply]
Well, it is a "physicist's theorem", so it basically encapsulates in shorthand a shared understanding of the community,what appears like a mere discussion to the outsider..... the theorem is the first paragraph of that section, but for the first and last sentences, which are explanatory qualifications. A pithy maxim encapsulation of it, like "Spontaneously broken symmetries require scalar particles/excitations with the quantum numbers of the broken Lie generators" would be impenetrable to the skimmer. A Longer discussion would appear like an even more defocusing cheat.... But if you could improve the extant compromise, you might give it a shot. Cuzkatzimhut (talk) 01:11, 30 December 2010 (UTC)[reply]
Ok, fair enough. I guess just take this for what it is: the first impression of a non-expert reader. There seemed to be something missing from the article, but if you don't think that impression can be avoided, I'll take your word for it. --Doradus (talk) 15:40, 30 December 2010 (UTC)[reply]
OK, I'm not sure this is substantial help, but I italicized the core of the Theorem. You are implicitly right that the pompous simulation of math theorems in physics can often produce more confusion, by its invitation of nitpicking parsing, and might be deprecated. In another world, one might call it "Goldstone's Principle". As indicated, the Theorem/principle extends to fermion generators, or generators which are not scalar, so then even more frustrating to the meticulous parser of the formal principle stated. Cuzkatzimhut (talk) 19:07, 30 December 2010 (UTC)[reply]
Resisting hostile takeover by "the party of Higgs"[edit]
I disagree quite strongly with blasting the reference list with Higgs-mechanism
references, like the four 1964 papers inserted by Moose-32. They are historically important papers, to be sure, but anyone interested in the Higgs mechanism should
click the wikilink in place and read up on the Higgs mechanism; and, thence, click
on these primary references, if still interested. It is appropriate for the Goldstone boson article to conclude with its most celebrated exception, the Higgs mechanism, as it does at present, to summarize the nature of that exception, in broad terms, and to refer the reader to that article. But the original references shed no light on the Goldstone theorem, unless the reader has also appreciated the counter-intuitive mooting introduced by the gauge fields, which far outranges the scope of the article: this is precisely why there is a Higgs mechanism article. After monitoring the odd campaign-style spread of the 1964 PRL symmetry breaking papers, and the over-politicized links to it, my judgment and proposal is to take these four references down from here after a while, subject to scholarly discussion started here. Cuzkatzimhut (talk) 14:18, 30 March 2011 (UTC)[reply]
Hostile takeover from the party of Goldstone Theorem now, or is it the party of Goldstone boson, instead? Today's magnificently ill-considered idea. After ritual abuse in the hands of the "eaten Goldstons" crowd, and the "we lost our Goldstons" crowd, we now have the "liberate Goldstons from the damn theorem!" proposal. The hapless reader rushes someplace, anywhere, to at last figure out what the voodoo summaries of the Higgs mechanism drivel promise, and the symmetry breaking articles illustrate, poorly; and yet another vehicle for fragmentation of attention and appreciation of the mechanism is put forward. I strongly believe Goldstone's theorem and NGBs should stay in the same place, under one roof, possibly in different sections, as many as desired (But let me be clear that, to my taste, there are already far too many sections on exceptions, complications, and ill-considered self-serving defocussers. There is no excuse for the semantic infiltration exemplified by Higgs field (classical).)
If someone has a salutary idea of improving the article (for which there is more than plenty of room, considering Kibble's wonderful article in Scholarpedia) let them go ahead. But spawning off yet a different article on top of the ones just described and designed to frustrate the curious reader from getting to the bottom of the problem all but ensures permanent institutionalized mediocrity in this effort. It is a shame a large number of informed, well-meaning people, can end up achieving such an obviously dismal outcome. Cuzkatzimhut (talk) 00:28, 31 March 2013 (UTC)[reply]
I like the statement "However, two different spontaneously broken generators may now give rise to the same Nambu–Goldstone boson." in the "Nonrelativistic theories" section. To make this section more precise, I think it is better to distinguish two different mechanisms for the "many to 1" correspondence between broken generators and Goldstone bosons:
[1] As the current article correctly describes, when in the case of spacetime symmetries, "Goldstone modes for some generators might be expressed as gradients of Goldstone modes for other broken generators." A superfluid is indeed the good example (SSB of U(1) and Galilean). A crystal lattice (SSB of translation and rotation) is also worth mentioned. I think we should add some references, for example,
I. Low and A. V. Manohar, Phys. Rev. Lett. 88, 101602 (2002).
[2] Even for internal symmetries, it is possible that two Goldstone fields form a canonically conjugate pairs, reducing the number of independent gapless modes. In this case, missing Goldstone modes cannot be expressed by gradient of other goldstone modes. A ferromagnet is the best known example of this type. The good references for this will be
User:Ramzuiv reverted a parenthetical statement linking to the Higgs mechanism of absorbing Goldstone boson degrees of freedom into empty polarization states of gauge bosons. Universally, and for over half a century, the shared metaphor "eaten" has been employed in the physics community, and this is not the place to object to it. Operators do eat operators in the technical sense detailed in the linked article. In fact, the very same eating metaphor is the last example undergirding the elaborate structure of the weak interactions. It is inappropriate and confusing to expect precise technical outlines in this article, when the link to this very "eating" of operators is right there for the interested, well meaning, reader to go to and inform himself. I strongly believe that discussion of the Higgs mechanism does not belong here, but should be confined to its adequate specialized article.
This is part of resisting takeover by the "party of Higgs", discussed above. The point is the parenthetical statement, ideally a footnote (you wish to demote it to such?), covers a breathtaking loophole in Goldstone's theorem, and, strictly speaking, there are no Goldstone bosons in such systems anymore... even though a trained ear hears the duck's voice coming from the wolf's belly, with proper attribution to Prokofiev. The parenthetical sentence is meant to dispatch the reader who is in this article in error, when he would rather learn about the Higgs mechanism.
Please do not indulge in extended discussions in the comment lines of the edits. Cuzkatzimhut (talk) 00:42, 10 December 2019 (UTC)[reply]
I neither want to see, nor intended to ask for, a precise technical outline of the Higgs mechanism in this article. You and I are of the same mind when it comes to that issue. What I was asking for was to replace the word 'eaten' with a clearer word (for example, "absorbed", as you propose). It is appropriate for me to object to the usage of a badly used metaphor here, regardless of it being one that is commonly employed by physicists. A metaphor fails when it fails. In this sense, it is not a metaphor (since - as we both want - this article does not explain how the 'eating' works. A metaphor is an aid for the explanation which belongs on a different page), but rather it is jargon - a physicist talking to another physicist will be familiar with the metaphor of the Higgs mechanism "eating" a Goldstone boson, having heard it in class in a context where it made sense, but a layman (who we must remember, is part of the diverse target audience of (nearly) every Wikipedia article - including this one) will simply be left scratching their head. I propose changing the sentence in question to "Their degrees of freedom are absorbed by the Higgs mechanism" or alternatively "removed", if you feel it would be more appropriate. If you feel that there is value to be had in maintaining the reference to the familiar metaphor, "are absorbed ("eaten") by the Higgs mechanism" will also work well. I would also like to see the other mention of "eaten", that comes right after the footnote, changed similarly.
I do acknowledge that it would have been appropriate for me to have left a note here on the talk page earlier, and it was careless of me to remove the parenthetical, since it is genuinely useful. That being said, I stand by boldly placing the clarify tag back, since my intention, as I highlighted both in my original edit and in the comment of my reversion, was not fulfilled, and I further felt that my original judgement (that "eaten" should be replaced by a better word - as you offered, "absorbed" works well) was correct, even after your edit.
All the best, Ramzuiv (talk) 04:58, 10 December 2019 (UTC)[reply]
Thank you for acknowledging that Wikipedia articles should be at least somewhat understandable to the layman. But the assumption that all physicists understand the term "eaten" may be exaggerated. Physicists who specialize in other areas such as general relativity may not have been fully educated in concepts such as the Higgs mechanism, especially if they studied long ago. I found the entire article somewhat obscure, being one who studies general relativity, but suddenly needs to know how a graviton might be considered a Goldstone boson. In particular, I needed to know whether a Goldstone boson can be viewed as a wave, and what wave equation it would satisfy, if so. The article was only slightly helpful at this level. 97.73.101.77 (talk) 22:00, 4 August 2021 (UTC)Kathleen Rosser, https://quemadojournal.org[reply]
As discussed, this is the absolutely worst venue for discussing the Higgs mechanism--and gravity has little to do with it. A plain Goldstone boson is a massless excitation, as stated clearly in the article, so, of course, it is described by massless wave equations. However, WP is not a forum: I strongly believe you should be asking these questions in sites like PSE! Further see here. Cuzkatzimhut (talk) 15:49, 5 August 2021 (UTC)[reply]
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. Maliz 19:49, 5 November 2006 (UTC)
