1964 PRL symmetry breaking papers

Scientific research articles PRL 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 theories. These three papers were written by: Robert Brout and François Englert;Brout R. Englert F. 1998 Spontaneous Symmetry Breaking in Gauge Theories: A Historical Survey hep-th/9802142 Peter Higgs; and Gerald Guralnik, C. Richard Hagen, and Tom Kibble (GHK). They are credited with the theory of the Higgs mechanism and the prediction of the 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 showed how gauge bosons can acquire non-zero masses as a result of spontaneous symmetry breaking within gauge invariant models of the universe. 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 PRLs 50th anniversary celebration.Blume M. Brown S. Millev Y. 2008 http://prl.aps.org/50years/milestones#1964 Letters from the past, a PRL retrospective (1964) Physical Review Letters 2010-01-30 All of the six physicists were awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work;2010 http://www.aps.org/units/dpf/awards/sakurai.cfm J. J. Sakurai Prize Winners American Physical Society 2010-01-30 https://web.archive.org/web/20100212025108/http://www.aps.org/units/dpf/awards/sakurai.cfm 12 February 2010 live Brout, Englert and Higgs received the 2004 Wolf Prize in Physics;Dumé Isabelle 2004-01-20 Wolf prize goes to particle theorists https://physicsworld.com/a/wolf-prize-goes-to-particle-theorists/ 2024-04-10 Physics World en-GB and in 2013 Englert and Higgs received the Nobel Prize in Physics.https://www.nobelprize.org/nobel_prizes/physics/laureates/2013/ The Nobel Prize in Physics 2013 On 4 July 2012, the two main experiments at the Large Hadron Collider (ATLAS and CMS) at CERN confirmed independently the existence of a previously unknown particle with a mass of about 125 GeV/c2 (about 133 proton masses, on the order of 10−25 kg), which is "consistent with the Higgs boson" and widely believed to be the Higgs boson.4 July 2012 CERN experiments observe particle consistent with long-sought Higgs boson http://press-archive.web.cern.ch/press-archive/PressReleases/Releases2012/PR17.12E.html CERN 2015-06-02 2016-03-25 https://web.archive.org/web/20160325050100/http://press-archive.web.cern.ch/press-archive/PressReleases/Releases2012/PR17.12E.html dead Introduction In the mid-20th century, physicists were developing a mathematical framework to describe the fundamental particles and forces of nature, a concept known as gauge theory. This approach was very promising because it offered a way to build a consistent and comprehensive model of physics. A significant challenge, however, arose when trying to explain why some particles have mass. Early versions of these theories predicted that certain force-carrying particles should be massless, which contradicted experimental evidence. A major hurdle was a theoretical roadblock known as Goldstone's theorem. This theorem suggested that whenever a fundamental symmetry in a theory is "spontaneously broken"—a process necessary to give particles mass—new, unwanted massless particles must appear. The 1964 papers provided a crucial insight, showing how, in the specific case of gauge theories, Goldstone's theorem could be sidestepped. This allowed for the creation of theories where force-carrying particles could have mass without introducing these problematic massless particles. The solution they described is now known as the Higgs mechanism. History x150px  x150px The six authors of the 1964 PRL papers, who received the 2010 J. J. Sakurai Prize for their work. From left to right: Kibble, Guralnik, Hagen, Englert, Brout. Right: Higgs. 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 particles whose interactions are mediated by exchange particles known as force carriers. 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 field theories in which the objects of study are not particles and forces, but quantum fields and their symmetries.August 2012 However, 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 invariant approaches, including 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.Woit P. 13 November 2010 The Anderson–Higgs Mechanism https://www.math.columbia.edu/~woit/wordpress/?p=3282 Not Even Wrong Columbia University 2012-11-12 Goldstone's theorem, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions,Goldstone J. Salam A. Weinberg S. 1962 Broken Symmetries Physical Review 127 3 965–970 1962PhRv..127..965G 10.1103/PhysRev.127.965 since it appeared to show that zero-mass particles would have to also exist that were "simply not seen".Guralnik G. S. 2011 The Beginnings of Spontaneous Symmetry Breaking in Particle Physics — Derived From My on the Spot "Intellectual Battlefield Impressions" 1110.2253 physics.hist-ph According to Gerald Guralnik, physicists had "no understanding" how these problems could be overcome in 1964. In 2014, Guralnik and Carl Hagen wrote a paper that contended that even after 50 years there is still widespread misunderstanding, by physicists and the Nobel Committee, of the Goldstone boson role.Guralnik G. Hagen C. R. 2014 Where have all the Goldstone bosons gone? Modern Physics Letters A 29 9 1450046 1401.6924 2014MPLA...2950046G 10.1142/S0217732314500461 119257339 This paper, published in Modern Physics Letters A, turned out to be Guralnik's last published work.Hagen C. R. August 2014 Obituaries - Gerald Stanford Guralnik Physics Today 67 8 57–58 10.1063/PT.3.2488 free 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 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 confinement realized in 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 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] The Higgs mechanism is a process by which vector bosons can get rest mass without explicitly breaking gauge invariance, as a byproduct of spontaneous symmetry breaking.Kibble T. W. B. 2009 Englert–Brout–Higgs–Guralnik–Hagen–Kibble Mechanism (History) Scholarpedia 4 1 8741 2009SchpJ...4.8741K 10.4249/scholarpedia.8741 free The mathematical theory behind spontaneous symmetry breaking was initially conceived and published within particle physics by Yoichiro Nambu in 1960,The Nobel Prize in Physics 2008 – official Nobel Prize website. the concept that such a mechanism could offer a possible solution for the "mass problem" was originally suggested in 1962 by Philip Anderson,Higgs P. 24 November 2010 My Life as a Boson http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf King's College London https://web.archive.org/web/20140501135924/http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf 2014-05-01 dead – the original 2001 paper can be found at: Duff M. J. Liu J. T. 2003 2001 A Spacetime Odyssey: Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics https://books.google.com/books?id=ONhnbpq00xIC&pg=PA86 86–88 World Scientific Publishing 978-981-238-231-34–5Anderson P. 1963 Plasmons, gauge invariance and mass Physical Review 130 1 439 1963PhRv..130..439A 10.1103/PhysRev.130.439 and Abraham Klein and 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.Klein A. Lee B. 1964 Does Spontaneous Breakdown of Symmetry Imply Zero-Mass Particles? Physical Review Letters 12 10 266 1964PhRvL..12..266K 10.1103/PhysRevLett.12.266 These approaches were quickly developed into a full relativistic model, independently and almost simultaneously, by three groups of physicists: by François Englert and Robert Brout in August 1964;Englert F. Brout R. 1964 Broken Symmetry and the Mass of Gauge Vector Mesons Physical Review Letters 13 9 321–23 1964PhRvL..13..321E 10.1103/PhysRevLett.13.321 free by Peter Higgs in October 1964;Higgs P. 1964 Broken Symmetries and the Masses of Gauge Bosons Physical Review Letters 13 16 508–509 1964PhRvL..13..508H 10.1103/PhysRevLett.13.508 free and by Gerald Guralnik, Carl Hagen, and Tom Kibble (GHK) in November 1964.Guralnik G. Hagen C. R. Kibble T. W. B. 1964 Global Conservation Laws and Massless Particles Physical Review Letters 13 20 585–587 1964PhRvL..13..585G 10.1103/PhysRevLett.13.585 free Higgs also wrote a response published in September 1964 to an objection by Walter Gilbert,Kibble T. W. B. 2009 Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism Scholarpedia 4 1 6441 2009SchpJ...4.6441K 10.4249/scholarpedia.6441 free Higgs P. 1964 Broken symmetries, massless particles and gauge fields Physics Letters 12 2 132–133 1964PhL....12..132H 10.1016/0031-9163(64)91136-9 which showed that if calculating within the radiation gauge, Goldstone's theorem and Gilbert's objection would become inapplicable.Goldstone's theorem only applies to gauges having manifest Lorentz covariance, a condition that took time to become questioned. But the process of quantisation requires a 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. (Higgs later described Gilbert's objection as prompting his own paper.Higgs P. 24 November 2010 My Life as a Boson http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf King's College London 17 January 2013 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. dead https://web.archive.org/web/20140501135924/http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf 1 May 2014 ) Properties of the model were further considered by Guralnik in 1965,Guralnik G. S. 2011 Gauge Invariance and the Goldstone Theorem Modern Physics Letters A 26 19 1381–1392 1107.4592 2011MPLA...26.1381G 10.1142/S0217732311036188 118500709 by Higgs in 1966,Higgs P. 1966 Spontaneous Symmetry Breakdown without Massless Bosons Physical Review 145 4 1156–1163 1966PhRv..145.1156H 10.1103/PhysRev.145.1156 free by Kibble in 1967,Kibble 979-0-2600-0043-8 1967 Symmetry Breaking in Non-Abelian Gauge Theories Physical Review 155 5 1554–1561 1967PhRv..155.1554K 10.1103/PhysRev.155.1554 and further by GHK in 1967. 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.http://prl.aps.org/50years/milestones#1964 Physical Review Letters – 50th Anniversary Milestone Papers Physical Review Letters 2014-02-12 In 1967, Steven WeinbergWeinberg S. 1967 A Model of Leptons Physical Review Letters 19 21 1264–1266 1967PhRvL..19.1264W 10.1103/PhysRevLett.19.1264 free and Abdus SalamSalam A. Svartholm N. 1968 Elementary Particle Physics: Relativistic Groups and Analyticity 367 Eighth Nobel Symposium Almquvist and Wiksell Stockholm independently showed how a Higgs mechanism could be used to break the electroweak symmetry of Sheldon Glashow's unified model for the weak and electromagnetic interactionsGlashow S. L. 1961 Partial-symmetries of weak interactions Nuclear Physics 22 4 579–588 1961NucPh..22..579G 10.1016/0029-5582(61)90469-2 (itself an extension of work by Julian 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.Ellis J. Gaillard M. K. Nanopoulos D. V. A Historical Profile of the Higgs Boson 2012 1201.6045 hep-ph A field with the "Mexican hat" potential and has a minimum not at zero but at some non-zero value . By expressing the action in terms of the field (where is a constant independent of position), we find the Yukawa term has a component . Since both and are constants, this looks exactly like the mass term for a fermion of mass . The field is then the Higgs field. 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 renormalised. In 1971–1972, Martinus J, G, Veltman and Gerard 't Hooft proved renormalisation of Yang–Mills was possible in two papers covering massless, and then massive, fields. Their contribution, and others' work on the renormalization group, was eventually "enormously profound and influential",Politzer D. 2005 The Dilemma of Attribution https://www.nobelprize.org/nobel_prizes/physics/laureates/2004/politzer-lecture.html Les Prix Nobel. The Nobel Prizes 2004 85–95 Tore Frängsmyr Stockholm Nobel Foundation 22 January 2013 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. Also published in 10.1073/pnas.0501644102 The dilemma of attribution 2005 Politzer H. David Proceedings of the National Academy of Sciences 102 22 7789–7793 free 15911758 1142376 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 1971Coleman S. 1979 The 1979 Nobel Prize in Physics Science 206 4424 1290–1292 1979Sci...206.1290C 10.1126/science.206.4424.1290 17799637 – discussed by David Politzer in his 2004 Nobel speech. "Coleman 1979" – now the most cited in particle physicsLetters from the Past – A PRL Retrospective (50 year celebration, 2008) – and even in 1970 according to David Politzer, Glashow's teaching of the weak interaction contained no mention of Weinberg's, Salam's, or Glashow's own work. In practice, Politzer states, almost everyone learned of the theory due to physicist Benjamin Lee, who combined the work of Veltman and 't Hooft with insights by others, and popularised the completed theory. In this way, from 1971, interest and acceptance "exploded"  and the ideas were quickly absorbed in the mainstream. 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 positions. 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.Guralnik G. S. Hagen C. R. Kibble T. W. B. 1967 Broken Symmetries and the Goldstone Theorem http://www.physics.princeton.edu/~mcdonald/examples/EP/guralnik_ap_2_567_67.pdf Cool R. L. Rodney L. Cool Marsha R. E. Advances in Physics Interscience Publishers 2 567–708 978-0-470-17057-1 2014-09-16 2015-09-24 https://web.archive.org/web/20150924072804/http://www.physics.princeton.edu/~mcdonald/examples/EP/guralnik_ap_2_567_67.pdf dead Summary and impact of the PRL papers The three papers written in 1964 were each recognised as milestone papers during Physical Review Letters 50th anniversary celebration. Their six authors were also awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work.http://www.aps.org/units/dpf/awards/sakurai.cfm J. J. Sakurai Prize for Theoretical Particle Physics American Physical Society 2016-09-16 (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.Merali Z. 4 August 2010 Physicists get political over Higgs https://www.nature.com/news/2010/100804/full/news.2010.390.html Nature Magazine 28 December 2011 ) Two of the three PRL papers (by Higgs and by GHK) contained equations for the hypothetical field that eventually would become known as the Higgs field and its hypothetical quantum, the Higgs boson. 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.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.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 and vector bosons". (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.Close F. 2011 The Infinity Puzzle: Quantum Field Theory and the Hunt for an Orderly Universe Oxford University Press 978-0-19-959350-7154, 166, 175) In the paper by GHK the boson is massless and decoupled from the massive states. 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 bosons in the model and to give a complete analysis of the general Higgs mechanism.Guralnik G. S. 2009 The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles International Journal of Modern Physics A 24 14 2601–2627 0907.3466 2009IJMPA..24.2601G 10.1142/S0217751X09045431 16298371 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. In addition to explaining how mass is acquired by vector bosons, the Higgs mechanism also predicts the ratio between the W boson and Z boson masses as well as their couplings with each other and with the Standard Model quarks and leptons.August 2012 Subsequently, many of these predictions have been verified by precise measurements performed at the Large Electron-Positron Collider (LEP) and the Standford Linear Collider (SLC) colliders, thus overwhelmingly confirming that some kind of Higgs mechanism does take place in nature,LEP Electroweak Working Group http://lepewwg.web.cern.ch/LEPEWWG/ but the exact manner by which it happens has not yet been discovered.August 2012 The results of searching for the Higgs boson are expected to provide evidence about how this is realized in nature.August 2012 Consequences of the papers The resulting electroweak theory and Standard Model have correctly predicted (among other discoveries) weak neutral currents, three bosons, the top and charm quarks, and with great precision, the mass and other properties of some of these.The success of the Higgs based electroweak theory and Standard Model is illustrated by their predictions of the mass of two particles later detected: the W boson (predicted mass: 80.390 0.018 GeV/c2, experimental measurement: 80.387 0.019 GeV/c2), and the Z boson (predicted mass: 91.1874 0.0021 GeV/c2, experimental measurement: 91.1876 0.0021 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 and charm quarks, all later proven to exist as the theory said. Many of those involved eventually won Nobel Prizes 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".Bernstein J. 1974 Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that http://www.calstatela.edu/faculty/kaniol/p544/rmp46_p7_higgs_goldstone.pdf Reviews of Modern Physics 46 1 7–48 1974RvMP...46....7B 10.1103/revmodphys.46.7 2012-12-10 dead https://web.archive.org/web/20130121121537/http://www.calstatela.edu/faculty/kaniol/p544/rmp46_p7_higgs_goldstone.pdf 2013-01-21 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." Lucio J. L. Zepeda A. 1987 Proceedings of the II Mexican School of Particles and Fields, Cuernavaca-Morelos, 1986 World Scientific 978-9971504342 29 https://books.google.com/books?id=jJ-yAAAAIAAJ&q=higgs+%22central+problem+today+in+particle+physics%22Gunion J. F. Dawson H. E. Kane G. Haber S. 1990 The Higgs Hunter's Guide Perseus Publishing 11 (?) https://books.google.com/books?id=M5moXN_SA-MC&q=central&pg=PA10 9780786743186 June 2024 InternetArchiveBot yes – 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. See also 30em Symmetry breaking Large Hadron Collider Fermilab Tevatron The God Particle, a popular science book on the Higgs boson, written by Leon M. Lederman Notes Note References 35em Further reading Nambu Y. Jona-Lasinio G. 10.1103/PhysRev.122.345 Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I Physical Review 122 1 345–358 1961 1961PhRv..122..345N free Anderson P. 10.1103/PhysRev.130.439 Plasmons, Gauge Invariance, and Mass Physical Review 130 439–442 1963 1 1963PhRv..130..439A Gilbert W. Broken Symmetries and Massless Particles 10.1103/PhysRevLett.12.713 Physical Review Letters 12 25 713–714 1964 1964PhRvL..12..713G Guralnik G. 2013 Heretical Ideas that Provided the Cornerstone for the Standard Model of Particle Physics https://www.sps.ch/fileadmin/_migrated/content_uploads/Mitteilungen.39.pdf SPG Mitteilungen 39 14–16 M. T. CP-Violation in the Renormalizable Theory of Weak Interaction Progress of Theoretical Physics 49 2 Kobayashi 652–657 1973 10.1143/PTP.49.652 Maskawa 1973PThPh..49..652K free 2433/66179 free 't Hooft G. Veltman M. 10.1016/0550-3213(72)90279-9 Regularization and renormalization of gauge fields Nuclear Physics B 44 1 189–213 1972 1972NuPhB..44..189T 1874/4845 https://repositorio.unal.edu.co/handle/unal/81144 free External links The Hunt for the Higgs at Tevatron CERN Courier Letter from GHK – December 2008 https://web.archive.org/web/20120220104152/http://cerncourier.com/cws/article/cern/36683 2012-02-20 In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking https://web.archive.org/web/20161110005400/http://cerncourier.com/cws/article/cern/32522 2016-11-10 Blog Not Even Wrong, Review of Massive by Ian Sample Blog Not Even Wrong, Anderson-Higgs Mechanism Ian Sample on Controversy and Nobel Reform https://web.archive.org/web/20200109123922/http://www.iansample.com/site/?q=content%2Fhiggs-row-and-nobel-reform 2020-01-09 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