Просмотр кода страницы Английская Википедия:1964 PRL symmetry breaking papers

{{Английская Википедия/Панель перехода}}
{{Italic title|string=PRL}}
{{Technical|date=March 2019}}
The '''1964 ''PRL'' symmetry breaking papers''' were written by three teams who proposed related but different approaches to explain how mass could arise in local [[gauge theory|gauge theories]]. These three papers were written by: [[Robert Brout]] and [[François Englert]];<ref name="eb64" /><ref>
{{cite arXiv
 |last1=Brout |first1=R.
 |last2=Englert |first2=F.
 |year=1998
 |title=Spontaneous Symmetry Breaking in Gauge Theories: A Historical Survey
 |eprint=hep-th/9802142
}}</ref> [[Peter Higgs]];<ref name="higgs64" /> and [[Gerald Guralnik]], [[C. R. Hagen|C. Richard Hagen]], and [[Tom W. B. Kibble|Tom Kibble]] (GHK).<ref name="ghk64" /><ref name="Guralnik 2009" /> They are credited with the theory of the [[Higgs mechanism]] and the prediction of the [[Higgs boson|Higgs field and Higgs boson]]. Together, these provide a theoretical means by which [[Goldstone's theorem]] (a problematic limitation affecting early modern [[particle physics]] theories) can be avoided. They show how [[gauge bosons]] can acquire non-zero masses as a result of [[spontaneous symmetry breaking]] within [[gauge invariance|gauge invariant]] models of the universe.<ref name="ScholarpediaKibble" /> 

As such, these form the key element of the [[electroweak theory]] that forms part of the [[Standard Model]] of [[particle physics]], and of many models, such as the [[Grand Unified Theory]], that go beyond it. The papers that introduce this mechanism were published in ''[[Physical Review Letters]]'' (''PRL'') and were each recognized as milestone papers by ''PRL''{{'}}s 50th anniversary celebration.<ref>
{{cite web
 |last1=Blume |first1=M.
 |last2=Brown |first2=S.
 |last3=Millev |first3=Y.
 |year=2008
 |url=http://prl.aps.org/50years/milestones#1964
 |title=Letters from the past, a PRL retrospective (1964)
 |publisher=[[Physical Review Letters]]
 |access-date=2010-01-30
 }}</ref> All of the six physicists were awarded the 2010 [[Sakurai Prize|J. J. Sakurai Prize for Theoretical Particle Physics]] for this work,<ref>
{{cite web
 |year=2010
 |url=http://www.aps.org/units/dpf/awards/sakurai.cfm
 |title=J. J. Sakurai Prize Winners
 |publisher=[[American Physical Society]]
 |access-date=2010-01-30
 |archive-url=https://web.archive.org/web/20100212025108/http://www.aps.org/units/dpf/awards/sakurai.cfm
 |archive-date=12 February 2010
 |url-status=live
}}</ref> and in 2013 Englert and Higgs received the Nobel Prize in Physics.<ref>{{Cite web | url=https://www.nobelprize.org/nobel_prizes/physics/laureates/2013/ | title=The Nobel Prize in Physics 2013}}</ref>

On 4 July 2012, the two main experiments at the LHC ([[ATLAS experiment|ATLAS]] and [[Compact Muon Solenoid|CMS]]) both reported independently the confirmed existence of a previously unknown particle with a mass of about {{val|125|ul=GeV/c2}} (about 133 proton masses, on the order of 10<sup>−25</sup>&nbsp;kg), which is "consistent with the Higgs boson" and widely believed to be the Higgs boson.<ref name=cern1207>{{cite press release
 |date=4 July 2012
 |title=CERN experiments observe particle consistent with long-sought Higgs boson
 |url=http://press-archive.web.cern.ch/press-archive/PressReleases/Releases2012/PR17.12E.html
 |publisher=[[CERN]]
 |access-date=2015-06-02
 |archive-date=2016-03-25
 |archive-url=https://web.archive.org/web/20160325050100/http://press-archive.web.cern.ch/press-archive/PressReleases/Releases2012/PR17.12E.html
 |url-status=dead
 }}</ref>

== Introduction ==
A [[gauge theory]] of [[elementary particles]] is a very attractive potential framework for constructing the [[grand unified theory|ultimate theory]]. Such a theory has the very desirable property of being potentially [[renormalization|renormalizable]]—shorthand for saying that all calculational infinities encountered can be consistently absorbed into a few parameters of the theory. However, as soon as one gives mass to the gauge fields, renormalizability is lost, and the theory rendered useless. [[Spontaneous symmetry breaking]] is a promising mechanism, which could be used to give mass to the vector gauge particles. A significant difficulty which one encounters, however, is [[Goldstone's theorem]], which states that in any [[quantum field theory]] which has a spontaneously broken symmetry there must occur a zero-mass particle. So the problem arises—how can one break a [[symmetry]] and at the same time not introduce unwanted zero-mass particles. The resolution of this dilemma lies in the observation that in the case of gauge theories, the Goldstone theorem can be avoided by working in the so-called [[radiation gauge]]. This is because the proof of Goldstone's theorem requires manifest [[Lorentz covariance]], a property not possessed by the radiation gauge.

== History ==
{| class="wikitable" style="float:right; margin:0 0 1em 1em; font-size:85%; width:354px;"
|-
| {{nowrap|[[File:AIP-Sakurai-best.JPG|x150px]]&nbsp;&nbsp;[[File:Higgs, Peter (1929) cropped.jpg|x150px]]}}<br />
The six authors of the 1964 ''PRL'' papers, who received the 2010 [[Sakurai Prize|J. J. Sakurai Prize]] for their work. From left to right: [[T. W. B. Kibble|Kibble]], [[Gerald Guralnik|Guralnik]], [[C. R. Hagen|Hagen]], [[François Englert|Englert]], [[Robert Brout|Brout]]. ''Right:'' [[Peter Higgs|Higgs]].
|}
{{wikinews|has=news related to| 2010 Sakurai Prize awarded for 1964 Higgs Boson theory work| Prospective Nobel Prize for Higgs boson work disputed}}
Particle physicists study [[matter]] made from [[fundamental particle]]s whose interactions are mediated by exchange particles known as [[force carrier]]s. At the beginning of the 1960s a number of these particles had been discovered or proposed, along with theories suggesting how they relate to each other, some of which had already been reformulated as [[quantum field theory|field theories]] in which the objects of study are not particles and forces, but [[quantum field]]s and their [[Symmetry (physics)|symmetries]].{{citation needed|date=August 2012}} However, [[Unified field theory|attempts to unify]] known [[fundamental forces]] such as the [[electromagnetic force]] and the [[weak nuclear force]] were known to be incomplete. One known omission was that [[gauge invariance|gauge invariant]] approaches, including [[non-abelian gauge theory|non-abelian]] models such as [[Yang–Mills theory]] (1954), which held great promise for unified theories, also seemed to predict known massive particles as massless.<ref name=woit>
{{cite web
 |last=Woit |first=P.
 |date=13 November 2010
 |title=The Anderson–Higgs Mechanism
 |url=http://www.math.columbia.edu/~woit/wordpress/?p=3282
 |work=Not Even Wrong
 |publisher=[[Columbia University]]
 |access-date=2012-11-12
}}</ref> [[Goldstone's theorem]], relating to [[continuous symmetry|continuous symmetries]] within some theories, also appeared to rule out many obvious solutions,<ref>
{{cite journal
 |last1=Goldstone |first1=J.
 |last2=Salam |first2=A.
 |last3=Weinberg |first3=S.
 |year=1962
 |title=Broken Symmetries
 |journal=[[Physical Review]]
 |volume=127 |issue=3 |pages=965–970
 |bibcode=1962PhRv..127..965G
 |doi=10.1103/PhysRev.127.965
}}</ref> since it appeared to show that zero-mass particles would have to also exist that were "simply not seen".<ref name="Guralnik 2011">
{{cite arXiv
 |last=Guralnik |first=G. S.
 |year=2011
 |title=The Beginnings of Spontaneous Symmetry Breaking in Particle Physics — Derived From My on the Spot "Intellectual Battlefield Impressions"
 |eprint=1110.2253
 |class=physics.hist-ph
}}</ref> According to [[Gerald Guralnik]], physicists had "no understanding" how these problems could be overcome in 1964.<ref name="Guralnik 2011" /> In 2014, Guralnik and [[C. R. Hagen|Carl Hagen]] wrote a paper that contended that even after 50 years there is still widespread misunderstanding, by [[physicist]]s and the [[Nobel Committee for Physics|Nobel Committee]], of the [[Goldstone boson]] role.<ref name="Guralnik2014">
{{cite journal
 |last1=Guralnik |first1=G.
 |last2=Hagen |first2=C. R.
 |year=2014
 |title=Where have all the Goldstone bosons gone?
 |journal=[[Modern Physics Letters A]]
 |volume=29 |issue=9 |page=1450046
 |arxiv=1401.6924
 |bibcode=2014MPLA...2950046G
 |doi=10.1142/S0217732314500461
|s2cid=119257339
 }}</ref> This paper, published in ''[[Modern Physics Letters A]]'', turned out to be Guralnik's last published work.<ref>
{{cite journal
 |last1=Hagen |first1=C. R.
 |date=August 2014
 |title=Obituaries - Gerald Stanford Guralnik
 |journal=[[Physics Today]]
 |volume=67 |issue=8 |pages=57–58
 |doi=10.1063/PT.3.2488
|doi-access=free
 }}</ref>

Particle physicist and mathematician [[Peter Woit]] summarised the state of research at the time:
: "Yang and Mills work on non-abelian gauge theory had one huge problem: in [[perturbation theory (quantum mechanics)|perturbation theory]] it has massless particles which don't correspond to anything we see. One way of getting rid of this problem is now fairly well-understood, the phenomenon of [[color confinement|confinement]] realized in [[quantum chromodynamics|QCD]], where the strong interactions get rid of the massless "gluon" states at long distances. By the very early sixties, people had begun to understand another source of massless particles: spontaneous symmetry breaking of a continuous symmetry. What [[Philip Warren Anderson|Philip Anderson]] realized and worked out in the summer of 1962 was that, when you have ''both'' gauge symmetry ''and'' spontaneous symmetry breaking, the Nambu–Goldstone massless mode can combine with the massless gauge field modes to produce a physical massive vector field. This is what happens in [[superconductivity]], a subject about which Anderson was (and is) one of the leading experts." ''[text condensed]'' <ref name="woit" />

The [[Higgs mechanism]] is a process by which [[vector boson]]s can get [[rest mass]] ''without'' [[explicit symmetry breaking|explicitly breaking]] [[gauge invariance]], as a byproduct of [[spontaneous symmetry breaking]].<ref name="ScholarpediaKibble"/><ref name="scholarpedia_a">
{{cite journal
 |last=Kibble |first=T. W. B.
 |year=2009
 |title=Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism (History)
 |journal=[[Scholarpedia]]
 |volume=4 |issue=1 |page=8741
 |bibcode=2009SchpJ...4.8741K
 |doi=10.4249/scholarpedia.8741
|doi-access=free
 }}</ref> The mathematical theory behind spontaneous symmetry breaking was initially conceived and published within particle physics by [[Yoichiro Nambu]] in 1960,<ref name="nambu nobel">[https://www.nobelprize.org/nobel_prizes/physics/laureates/2008 The Nobel Prize in Physics 2008] – official Nobel Prize website.</ref> the concept that such a mechanism could offer a possible solution for the "mass problem" was originally suggested in 1962 by [[Philip Warren Anderson|Philip Anderson]],<ref name="MyLifeAsABoson">
{{cite web
 |last=Higgs |first=P.
 |date=24 November 2010
 |title=My Life as a Boson
 |url=http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf
 |publisher=[[King's College London]]
 |archive-url=https://web.archive.org/web/20140501135924/http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf
 |archive-date=2014-05-01
 |url-status=dead
}} – the original 2001 paper can be found at: {{cite book
 |editor1-last=Duff |editor1-first=M. J.
 |editor2-last=Liu |editor2-first=J. T.
 |year=2003
 |title=2001 A Spacetime Odyssey: Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics
 |url=https://books.google.com/books?id=ONhnbpq00xIC&pg=PA86
 |pages=86–88
 |publisher=[[World Scientific Publishing]]
 |isbn=978-981-238-231-3
}}</ref>{{rp|4–5}}<ref>
{{cite journal
 |last1=Anderson  |first1=P.
 |year=1963
 |title=Plasmons, gauge invariance and mass
 |journal=[[Physical Review]]
 |volume=130 |issue=1
 |page=439
 |bibcode=1963PhRv..130..439A
 |doi=10.1103/PhysRev.130.439
}}</ref> and [[Abraham Klein (physicist)|Abraham Klein]] and [[Benjamin W. Lee|Benjamin Lee]] showed in March 1964 that Goldstone's theorem could be avoided this way in at least some non-relativistic cases and speculated it might be possible in truly relativistic cases.<ref>
{{Cite journal
 |last1=Klein |first1=A.
 |last2=Lee |first2=B.
 |year=1964
 |title=Does Spontaneous Breakdown of Symmetry Imply Zero-Mass Particles?
 |journal=[[Physical Review Letters]]
 |volume=12 |issue=10 |pages=266
 |bibcode=1964PhRvL..12..266K
 |doi=10.1103/PhysRevLett.12.266
}}</ref>

These approaches were quickly developed into a full [[Special relativity|relativistic]] model, independently and almost simultaneously, by three groups of physicists: by [[François Englert]] and [[Robert Brout]] in August 1964;<ref name="eb64">{{Cite journal
 |last1=Englert |first1=F.
 |last2=Brout |first2=R.
 |year=1964
 |title=Broken Symmetry and the Mass of Gauge Vector Mesons
 |journal=[[Physical Review Letters]]
 |volume=13 |issue=9 |pages=321–23
 |bibcode=1964PhRvL..13..321E
 |doi=10.1103/PhysRevLett.13.321
|doi-access=free
 }}</ref> by [[Peter Higgs]] in October 1964;<ref name="higgs64">
{{Cite journal
 |last=Higgs |first=P.
 |year=1964
 |title=Broken Symmetries and the Masses of Gauge Bosons
 |journal=[[Physical Review Letters]]
 |volume=13 |issue=16 |pages=508–509
 |bibcode=1964PhRvL..13..508H
 |doi=10.1103/PhysRevLett.13.508
|doi-access=free
 }}</ref> and by [[Gerald Guralnik]], [[C. R. Hagen|Carl Hagen]], and [[T. W. B. Kibble|Tom Kibble]] (GHK) in November 1964.<ref name="ghk64">
{{Cite journal
 |last1=Guralnik |first1=G.
 |last2=Hagen |first2=C. R.
 |last3=Kibble |first3=T. W. B.
 |year=1964
 |title=Global Conservation Laws and Massless Particles
 |journal=[[Physical Review Letters]]
 |volume=13 |issue=20 |pages=585–587
 |bibcode=1964PhRvL..13..585G
 |doi=10.1103/PhysRevLett.13.585 
|doi-access=free
 }}</ref> Higgs also wrote a response published in September 1964 to an objection by [[Walter Gilbert|Gilbert]],<ref name="ScholarpediaKibble">
{{Cite journal
 |last1=Kibble |first1=T. W. B.
 |year=2009 
 |title=Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism
 |journal=[[Scholarpedia]]
 |volume=4 |issue=1
 |page=6441
 |bibcode=2009SchpJ...4.6441K
 |doi=10.4249/scholarpedia.6441
|doi-access=free
 }}</ref><ref name="higgs64note">
{{Cite journal
 |last=Higgs |first=P.
 |year=1964
 |title=Broken symmetries, massless particles and gauge fields
 |journal=[[Physics Letters]]
 |volume=12 |issue=2 |pages=132–133
 |bibcode=1964PhL....12..132H
 |doi=10.1016/0031-9163(64)91136-9
}}</ref> which showed that if calculating within the radiation gauge, Goldstone's theorem and Gilbert's objection would become inapplicable.<ref group="Note" name="GoldstoneNote">[[Goldstone's theorem]] only applies to gauges having [[Lorentz covariance|manifest Lorentz covariance]], a condition that took time to become questioned. But the process of [[quantization (physics)|quantisation]]<!--BRITISH ENGLISH SPELLING--> requires a [[gauge fixing|gauge to be fixed]] and at this point it becomes possible to choose a gauge such as the 'radiation' gauge which is not invariant over time, so that these problems can be avoided.</ref> (Higgs later described Gilbert's objection as prompting his own paper.<ref>
{{cite web
 |last=Higgs 
 |first=P. 
 |date=24 November 2010 
 |title=My Life as a Boson 
 |url=http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf 
 |publisher=[[King's College London]] 
 |access-date=17 January 2013 
 |quote=Gilbert ... wrote a response to [Klein and Lee's paper] saying 'No, you cannot do that in a relativistic theory. You cannot have a preferred unit time-like vector like that.' This is where I came in, because the next month was when I responded to Gilbert's paper by saying 'Yes, you can have such a thing' but only in a gauge theory with a gauge field coupled to the current. 
 |url-status=dead 
 |archive-url=https://web.archive.org/web/20140501135924/http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf 
 |archive-date=1 May 2014 
}}</ref>) Properties of the model were further considered by Guralnik in 1965,<ref>
{{cite journal
 |last=Guralnik |first=G. S.
 |year=2011
 |title=Gauge Invariance and the Goldstone Theorem
 |journal=[[Modern Physics Letters A]]
 |volume=26 |issue=19 |pages=1381–1392
 |arxiv=1107.4592
 |bibcode=2011MPLA...26.1381G
 |doi=10.1142/S0217732311036188
 |s2cid=118500709
}}</ref> by Higgs in 1966,<ref>
{{Cite journal
 |last=Higgs |first=P.
 |year=1966
 |title=Spontaneous Symmetry Breakdown without Massless Bosons
 |journal=[[Physical Review]]
 |volume=145 |issue=4 |pages=1156–1163
 |bibcode=1966PhRv..145.1156H
 |doi=10.1103/PhysRev.145.1156
|doi-access=free
 }}</ref> by Kibble in 1967,<ref>
{{Cite journal
 |last=Kibble 979-0-2600-0043-8
 |year=1967
 |title=Symmetry Breaking in Non-Abelian Gauge Theories
 |journal=[[Physical Review]]
 |volume=155 |issue=5 |pages=1554–1561
 |bibcode=1967PhRv..155.1554K
 |doi=10.1103/PhysRev.155.1554
}}</ref> and further by GHK in 1967.<ref name=AdPhys2/> The original three 1964 papers showed that when a [[gauge theory]] is combined with an additional field that spontaneously breaks the symmetry, the gauge bosons can consistently acquire a finite mass.<ref name="ScholarpediaKibble"/><ref name="scholarpedia_a" /><ref name="prl">
{{Cite journal
 |url=http://prl.aps.org/50years/milestones#1964
 |title=Physical Review Letters&nbsp;– 50th Anniversary Milestone Papers
 |publisher=[[Physical Review Letters]]
|date=2014-02-12
 }}</ref> In 1967, [[Steven Weinberg]]<ref>
{{cite journal
 |last=Weinberg |first=S.
 |year=1967
 |title=A Model of Leptons
 |journal=[[Physical Review Letters]]
 |volume=19 |issue=21 |pages=1264–1266
 |bibcode=1967PhRvL..19.1264W
 |doi=10.1103/PhysRevLett.19.1264
|doi-access=free
 }}</ref> and [[Abdus Salam]]<ref>
{{cite conference
 |last=Salam |first=A.
 |editor-last=Svartholm |editor-first=N.
 |year=1968
 |book-title=Elementary Particle Physics: Relativistic Groups and Analyticity
 |pages=367
 |conference=Eighth Nobel Symposium
 |publisher=[[Almquvist and Wiksell]]
 |location=Stockholm
}}</ref> independently showed how a Higgs mechanism could be used to break the electroweak symmetry of [[Sheldon Glashow]]'s [[electroweak theory|unified model for the weak and electromagnetic interactions]]<ref>
{{cite journal
 |last=Glashow |first=S. L.
 |year=1961
 |title=Partial-symmetries of weak interactions
 |journal=[[Nuclear Physics (journal)|Nuclear Physics]]
 |volume=22 |issue=4 |pages=579–588
 |bibcode=1961NucPh..22..579G
 |doi=10.1016/0029-5582(61)90469-2
}}</ref> (itself an extension of work by [[Julian Schwinger|Schwinger]]), forming what became the [[Standard Model]] of particle physics. Weinberg was the first to observe that this would also provide mass terms for the fermions.<ref name="Ellis2012">
{{cite arXiv
 |last1=Ellis |first1=J.
 |last2=Gaillard |first2=M. K.
 |last3=Nanopoulos |first3=D. V.
 |title=A Historical Profile of the Higgs Boson
 |year=2012
 |eprint=1201.6045
 |class=hep-ph
}}</ref>&nbsp;{{#tag:ref|A field with the "Mexican hat" potential <math>V(\phi)=\mu^2\phi^2 + \lambda\phi^4</math> and <math>\mu^2 < 0</math> has a minimum not at zero but at some non-zero value <math>\phi_0</math>. By expressing the action in terms of the field <math>\tilde \phi=\phi-\phi_0</math> (where <math>\phi_0</math> is a constant independent of position), we find the Yukawa term has a component <math>g\phi_0 \bar\psi\psi</math>. Since both <math>g</math> and <math>\phi_0</math> are constants, this looks exactly like the mass term for a fermion of mass <math>g\phi_0</math>. The field <math>\tilde\phi</math> is then the [[Higgs field]].|group=Note}}

However, the seminal papers on spontaneous breaking of gauge symmetries were at first largely ignored, because it was widely believed that the (non-Abelian gauge) theories in question were a dead-end, and in particular that they could not be [[renormalizable|renormalised]]<!-- BRITISH ENGLISH SPELLING!-->. In 1971–1972, [[Martinus Veltman]] and [[Gerard 't Hooft]] proved renormalisation of Yang–Mills was possible in two papers covering massless, and then massive, fields.<ref name="Ellis2012"/> Their contribution, and others' work on the [[renormalization group]], was eventually "enormously profound and influential",<ref name="Politzer 2004">
{{cite journal
 |last=Politzer |first=D.
 |title=The Dilemma of Attribution
 |url=https://www.nobelprize.org/nobel_prizes/physics/laureates/2004/politzer-lecture.html
 |journal=Nobel Prize Lecture, 2004
 |year=2005
 |volume=102
 |issue=22
 |pages=7789–7793
 |publisher=[[Nobel Foundation]]
 |doi=10.1073/pnas.0501644102
 |pmid=15911758
 |pmc=1142376
 |access-date=22 January 2013
 |quote=Sidney Coleman published in ''Science'' magazine in 1979 a citation search he did documenting that essentially no one paid any attention to Weinberg's Nobel Prize winning paper until the work of 't Hooft (as explicated by Ben Lee). In 1971 interest in Weinberg's paper exploded. I had a parallel personal experience: I took a one-year course on weak interactions from Shelly Glashow in 1970, and he never even mentioned the Weinberg–Salam model or his own contributions.
|doi-access=free
 }}</ref> but even with all key elements of the eventual theory published there was still almost no wider interest. For example, [[Sidney Coleman]] found in a study that "essentially no-one paid any attention" to Weinberg's paper prior to 1971{{#tag:ref|
{{cite journal
 |last=Coleman |first=S.
 |year=1979
 |title=The 1979 Nobel Prize in Physics
 |journal=[[Science (magazine)|Science]]
 |volume=206 |issue=4424 |pages=1290–1292
 |bibcode=1979Sci...206.1290C
 |doi=10.1126/science.206.4424.1290
 |pmid=17799637
}} – discussed by [[David Politzer]] in his 2004 Nobel speech.<ref name="Politzer 2004"/>
 |name="Coleman 1979"
}} – now the most cited in particle physics<ref name="PRL_50years">[http://prl.aps.org/50years/milestones#1967 Letters from the Past – A PRL Retrospective] (50 year celebration, 2008)</ref> – and even in 1970 according to [[David Politzer|Politzer]], Glashow's teaching of the weak interaction contained no mention of Weinberg's, Salam's, or Glashow's own work.<ref name="Politzer 2004"/> In practice, Politzer states, almost everyone learned of the theory due to physicist [[Benjamin W. Lee|Benjamin Lee]], who combined the work of Veltman and 't Hooft with insights by others, and popularised the completed theory.<ref name="Politzer 2004"/> In this way, from 1971, interest and acceptance "exploded"&nbsp;<ref name="Politzer 2004"/> and the ideas were quickly absorbed in the mainstream.<ref name="Ellis2012"/><ref name="Politzer 2004"/>

=== The significance of requiring manifest covariance ===
Most students who have taken a course in [[electromagnetism]] have encountered the [[Coulomb potential]]. It basically states that two [[charged particles]] attract or repel each other by a force which varies according to the inverse square of their separation. This is fairly unambiguous for particles at rest, but if one or the other is following an arbitrary trajectory the question arises whether one should compute the force using the instantaneous positions of the particles or the so-called [[retarded potential|retarded position]]s. The latter recognizes that information cannot propagate instantaneously, rather it propagates at the [[speed of light]]. However, the [[radiation gauge]] says that one uses the instantaneous positions of the particles, but doesn't violate [[causality]] because there are compensating terms in the force equation. In contrast, the [[Lorenz gauge]] imposes [[manifest covariance]] (and thus causality) at all stages of a calculation. Predictions of observable quantities are identical in the two gauges, but the radiation gauge formulation of [[quantum field theory]] avoids [[Goldstone's theorem]].<ref name=AdPhys2>{{cite book
 |last1=Guralnik
 |first1=G. S.
 |last2=Hagen
 |first2=C. R.
 |last3=Kibble
 |first3=T. W. B.
 |year=1967
 |chapter=Broken Symmetries and the Goldstone Theorem
 |chapter-url=http://www.physics.princeton.edu/~mcdonald/examples/EP/guralnik_ap_2_567_67.pdf
 |editor1-last=Cool
 |editor1-first=R. L.
 |editor1-link=Rodney L. Cool
 |editor2-last=Marsha
 |editor2-first=R. E.
 |title=Advances in Physics
 |publisher=[[Interscience Publishers]]
 |volume=2
 |pages=567–708
 |isbn=978-0-470-17057-1
 |access-date=2014-09-16
 |archive-date=2015-09-24
 |archive-url=https://web.archive.org/web/20150924072804/http://www.physics.princeton.edu/~mcdonald/examples/EP/guralnik_ap_2_567_67.pdf
 |url-status=dead
 }}</ref>

=== Summary and impact of the ''PRL'' papers ===
The three papers written in 1964 were each recognised as milestone papers during ''[[Physical Review Letters]]''{{'s}} 50th anniversary celebration.<ref name="prl" /> Their six authors were also awarded the 2010 [[Sakurai Prize|J. J. Sakurai Prize for Theoretical Particle Physics]] for this work.<ref name="sakuraiprize">
{{cite web
 |url=http://www.aps.org/units/dpf/awards/sakurai.cfm
 |title=J. J. Sakurai Prize for Theoretical Particle Physics
 |publisher=[[American Physical Society]]
 |access-date=2016-09-16
}}</ref> (A controversy also arose the same year, because in the event of a [[Nobel Prize]] only up to three scientists could be recognised, with six being credited for the papers.<ref>
{{cite news
 |last=Merali |first=Z.
 |date=4 August 2010
 |title=Physicists get political over Higgs
 |url=http://www.nature.com/news/2010/100804/full/news.2010.390.html
 |newspaper=[[Nature Magazine]]
 |access-date=28 December 2011
}}</ref> ) Two of the three ''PRL'' papers (by Higgs and by GHK) contained equations for the hypothetical [[quantum field theory|field]] that eventually would become known as the Higgs field and its hypothetical [[quantum]], the Higgs boson.<ref name="higgs64" /><ref name="ghk64" /> Higgs's subsequent 1966 paper showed the decay mechanism of the boson; only a massive boson can decay and the decays can prove the mechanism.{{citation needed|date=August 2012}}

Each of these papers is unique and demonstrates different approaches to showing how mass arise in gauge particles. Over the years, the differences between these papers are no longer widely understood, due to the passage of time and acceptance of end-results by the [[particle physics]] community. A study of citation indices is interesting—more than 40 years after the 1964 publication in ''Physical Review Letters'' there is little noticeable pattern of preference among them, with the vast majority of researchers in the field mentioning all three milestone papers.{{citation needed|date=July 2012}}

In the paper by Higgs the boson is massive, and in a closing sentence Higgs writes that "an essential feature" of the theory "is the prediction of incomplete multiplets of [[scalar boson|scalar]] and [[vector boson]]s".<ref name="higgs64"/> ([[Frank Close]] comments that 1960s gauge theorists were focused on the problem of massless ''vector'' bosons, and the implied existence of a massive ''scalar'' boson was not seen as important; only Higgs directly addressed it.<ref name="frank_close_infinity_puzzle">
{{cite book
 |last=Close |first=F.
 |year=2011
 |title=The Infinity Puzzle: Quantum Field Theory and the Hunt for an Orderly Universe
 |publisher=[[Oxford University Press]]
 |isbn=978-0-19-959350-7
}}</ref>{{rp|154, 166, 175}}) In the paper by GHK the boson is massless and decoupled from the massive states.<ref name="ghk64" /> In reviews dated 2009 and 2011, Guralnik states that in the GHK model the boson is massless only in a lowest-order approximation, but it is not subject to any constraint and acquires mass at higher orders, and adds that the GHK paper was the only one to show that there are no massless [[Goldstone boson]]s in the model and to give a complete analysis of the general Higgs mechanism.<ref name="Guralnik 2011"/><ref name="Guralnik 2009">
{{cite journal
 |last1=Guralnik |first1=G. S.
 |year=2009
 |title=The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles
 |journal=[[International Journal of Modern Physics A]]
 |volume=24 |issue=14 |pages=2601–2627
 |arxiv=0907.3466
 |bibcode=2009IJMPA..24.2601G
 |doi=10.1142/S0217751X09045431
 |s2cid=16298371
}}</ref><ref name="Guralnik2014"/> All three reached similar conclusions, despite their very different approaches: Higgs' paper essentially used classical techniques, Englert and Brout's involved calculating vacuum polarization in perturbation theory around an assumed symmetry-breaking vacuum state, and GHK used operator formalism and conservation laws to explore in depth the ways in which Goldstone's theorem explicitly fails.<ref name="ScholarpediaKibble" />

In addition to explaining how mass is acquired by vector bosons, the Higgs mechanism also predicts the ratio between the [[W and Z bosons|W boson and Z boson]] masses as well as their [[coupling constant|couplings]] with each other and with the Standard Model quarks and leptons.{{citation needed|date=August 2012}} Subsequently, many of these predictions have been verified by precise measurements performed at the [[Large Electron–Positron Collider|LEP]] and the [[Stanford Linear Collider|SLC]] colliders, thus overwhelmingly confirming that some kind of Higgs mechanism does take place in nature,<ref name="EWWG">
{{cite web
 |title=LEP Electroweak Working Group
 |url=http://lepewwg.web.cern.ch/LEPEWWG/
}}</ref> but the exact manner by which it happens has not yet been discovered.{{citation needed|date=August 2012}} The results of searching for the Higgs boson are expected to provide evidence about how this is realized in nature.{{citation needed|date=August 2012}}

=== Consequences of the papers ===
The resulting electroweak theory and Standard Model have [[Standard Model#Tests and predictions|correctly predicted]] (among other discoveries) [[weak neutral current]]s, [[W and Z bosons|three bosons]], the [[top quark|top]] and [[charm quark]]s, and with great precision, the mass and other properties of some of these.<ref name="predictions" group="Note">The success of the Higgs based electroweak theory and Standard Model is illustrated by their [[Standard Model#Tests and predictions|predictions]] of the mass of two particles later detected: the W boson (predicted mass: {{val|80.390|0.018|ul=GeV/c2}}, experimental measurement: {{val|80.387|0.019|u=GeV/c2}}), and the Z boson (predicted mass: {{val|91.1874|0.0021|u=GeV/c2}}, experimental measurement: {{val|91.1876|0.0021|u=GeV/c2}}). The existence of the Z boson was itself another prediction. Other correct predictions included the [[weak neutral current]], the [[gluon]], and the [[top quark|top]] and [[charm quark]]s, all later proven to exist as the theory said.</ref> Many of those involved [[#Recognition and awards|eventually won]] [[Nobel Prize]]s or other renowned awards. A 1974 paper in ''[[Reviews of Modern Physics]]'' commented that "while no one doubted the [mathematical] correctness of these arguments, no one quite believed that nature was diabolically clever enough to take advantage of them".<ref>
{{cite journal
 |last=Bernstein 
 |first=J. 
 |year=1974 
 |title=Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that 
 |url=http://www.calstatela.edu/faculty/kaniol/p544/rmp46_p7_higgs_goldstone.pdf 
 |journal=[[Reviews of Modern Physics]] 
 |volume=46 
 |issue=1 
 |pages=7–48 
 |bibcode=1974RvMP...46....7B 
 |doi=10.1103/revmodphys.46.7 
 |access-date=2012-12-10 
 |url-status=dead 
 |archive-url=https://web.archive.org/web/20130121121537/http://www.calstatela.edu/faculty/kaniol/p544/rmp46_p7_higgs_goldstone.pdf 
 |archive-date=2013-01-21 
}}</ref> By 1986 and again in the 1990s it became possible to write that understanding and proving the Higgs sector of the Standard Model was "the central problem today in particle physics."&nbsp;<ref>
{{cite book
 |editor1-last=Lucio |editor1-first=J. L.
 |editor2-last=Zepeda |editor2-first=A.
 |year=1987
 |title=Proceedings of the II Mexican School of Particles and Fields, Cuernavaca-Morelos, 1986
 |publisher=[[World Scientific]]
 |isbn=978-9971504342
 |pages=29
 |url=https://books.google.com/books?id=jJ-yAAAAIAAJ&q=higgs+%22central+problem+today+in+particle+physics%22}}</ref><ref>
{{cite book
 |last1=Gunion |first1=J. F.
 |last2=Dawson |first2=H. E.
 |last3=Kane |first3=G.
 |last4=Haber |first4=S.
 |year=1990
 |title=The Higgs Hunter's Guide
 |publisher=[[Perseus Publishing]]
 |pages=11 (?)
 |url=https://books.google.com/books?id=M5moXN_SA-MC&q=central&pg=PA10
 |isbn=9780786743186
}} – quoted as being in the first (1990) edition of the book by Peter Higgs in his talk "My Life as a Boson", 2001, ref#25.</ref>

==See also==
{{columns-list|colwidth=30em|
*[[Symmetry breaking]]
*[[Large Hadron Collider]]
*[[Fermilab]]
*[[Tevatron]]
*''[[The God Particle: If the Universe Is the Answer, What Is the Question?|The God Particle]]'', a popular science book on the Higgs boson, written by [[Leon M. Lederman]]
}}

==Notes==
{{reflist|group=Note}}

==References==
{{reflist|35em}}

==Further reading==
{{refbegin}}
*{{Cite journal | last1 = Nambu | first1 = Y. | last2 = Jona-Lasinio | first2 = G. | doi = 10.1103/PhysRev.122.345 | title = Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I | journal = [[Physical Review]] | volume = 122 | issue = 1 | pages = 345–358 | year = 1961 |bibcode = 1961PhRv..122..345N | doi-access = free }}
*{{Cite journal | last1 = Anderson | first1 = P. | doi = 10.1103/PhysRev.130.439 | title = Plasmons, Gauge Invariance, and Mass | journal = [[Physical Review]] | volume = 130 | pages = 439–442 | year = 1963 | issue = 1 |bibcode = 1963PhRv..130..439A }}
*{{Cite journal | last1 = Gilbert | first1 = W. | title = Broken Symmetries and Massless Particles | doi = 10.1103/PhysRevLett.12.713 | journal = [[Physical Review Letters]] | volume = 12 | issue = 25 | pages = 713–714 | year = 1964 |bibcode = 1964PhRvL..12..713G }}
* {{cite journal |last=Guralnik |first=G. |year=2013 |title=Heretical Ideas that Provided the Cornerstone for the Standard Model of Particle Physics |url=http://www.sps.ch/fileadmin/_migrated/content_uploads/Mitteilungen.39.pdf |journal=[[SPG Mitteilungen]] |volume=39 |pages=14–16}}
*{{Cite journal| first1 = M.| first2 = T.| title = ''CP''-Violation in the Renormalizable Theory of Weak Interaction| journal = [[Progress of Theoretical Physics]] | volume = 49| issue = 2| last1 = Kobayashi| pages = 652–657| year = 1973| doi = 10.1143/PTP.49.652| last2 =    Maskawa|bibcode = 1973PThPh..49..652K | doi-access = free}}
*{{Cite journal | last1 = 't Hooft | first1 = G. | last2 = Veltman | first2 = M. | doi = 10.1016/0550-3213(72)90279-9 | title = Regularization and renormalization of gauge fields | journal = [[Nuclear Physics B]] | volume = 44 | issue = 1 | pages = 189–213 | year = 1972 |bibcode = 1972NuPhB..44..189T | hdl = 1874/4845 | url = https://repositorio.unal.edu.co/handle/unal/81144 | hdl-access = free }}
{{refend}}

==External links==
{{refbegin}}
*[http://apps3.aps.org/aps/meetings/april10/roser.pdf The Hunt for the Higgs at Tevatron]
*[http://cerncourier.com/cws/article/cern/36683 CERN Courier Letter from GHK – December 2008] {{Webarchive|url=https://web.archive.org/web/20120220104152/http://cerncourier.com/cws/article/cern/36683 |date=2012-02-20 }}
*[http://cerncourier.com/cws/article/cern/32522 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking]
*[http://www.math.columbia.edu/~woit/wordpress/?p=3266 Blog Not Even Wrong, Review of Massive by Ian Sample]
*[http://www.math.columbia.edu/~woit/wordpress/?p=3282 Blog Not Even Wrong, Anderson-Higgs Mechanism]
*[http://www.iansample.com/site/?q=content/higgs-row-and-nobel-reform Ian Sample on Controversy and Nobel Reform] {{Webarchive|url=https://web.archive.org/web/20200109123922/http://www.iansample.com/site/?q=content%2Fhiggs-row-and-nobel-reform |date=2020-01-09 }}
{{refend}}

{{DEFAULTSORT:1964 Prl Symmetry Breaking Papers}}
[[Category:1964 in science|PRL symmetry breaking papers]]
[[Category:Physics papers]]
[[Category:Works originally published in American magazines]]
[[Category:1964 documents]]
[[Category:Works originally published in science and technology magazines]]
[[Category:Standard Model]]
{{Навигационная таблица/Портал/Английская Википедия}}
[[Категория:Английская Википедия]]
[[Категория:Википедия]]
[[Категория:Статья из Википедии]]
[[Категория:Статья из Английской Википедии]]