Talk:Goldstone boson

message: 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)
thread_title:  JeffBobFrank comment 

message: 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)
replies: text: 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)

text: 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)
thread_title:  Villatortilla comment 

message: 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)
replies: text: Done. Yevgeny Kats 18:28, 28 July 2006 (UTC)
thread_title: Rename to Goldstone boson

message: 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)
replies: text: Someone else (not me) has already uploaded the image . Maliz 19:49, 5 November 2006 (UTC)
replies: text:  Can somebody plot it in polar coordinates, so that ugly corner spikes go away?Likebox (talk) 21:00, 4 November 2008 (UTC)
replies: text:  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)
replies: text: Looks nice; labeling axes can only confuse, not clarify the paradigm. Cuzkatzimhut (talk)  —Preceding undated comment added 16:25, 11 September 2009 (UTC)
thread_title:  Plot of the "mexican hat" potential? 

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
thread_title:  State Goldstone's theorem 

message: 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)
thread_title:  Resisting hostile takeover by "the party of Higgs" 

message: 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
Y. Nambu, J. Stat. Phys. 115, 7 (2004).
H. Watanabe and H. Murayama, Phys. Rev. Lett. 108, 251602 (2012).  — Preceding unsigned comment added by 2607:F140:400:A003:7550:5CBD:176A:8211 (talk) 14:35, 7 May 2014 (UTC)
thread_title:  Nonrelativistic theories