### Le champ de Higgs : de la matière condensée aux particules élémentaires ... en passant par un espace condensat ?

**Trois points de vue sur un phénomène physique**

- Le boson de Higgs: c'est définitivement une nouvelle particule pour la physique expérimentale des hautes énergies;
- Le modèle de Englert-Brout-Higgs-Guralnik-Hagen-Kible-Migdal-Polyakov: c'est peut-être la trace d'une structure fine de l'espacetemps pour une physique théorique inspirée par la géométrie non commutative;
- Le mécanisme de brisure spontanée de la symétrie de jauge électrofaible à la Nambu-Goldstone-Anderson: c'est la manifestation d'un véritable éther quantique du point de vue de la physique phénoménologique de la matière condensée.

**Brève histoire du mécanisme (NGA)EBHGHKMP ...**

Following the introduction into particle physics of spontaneous global symmetry breaking into particle physics by Nambu [21] and the formulation of a simple field-theoretical model by Goldstone [22], as well as the interpretation by Anderson [23] of superconductivity in terms of a spontaneously-broken local U(1) symmetry, in 1964. several papers introduced spontaneously-broken local symmetry into particle physics.The initial paper by Englert and Brout [24] was followed a few weeks later by two papers written independently by Higgs: the fi rst pointing out that a technical obstacle to a four-dimensional extension of Anderson's approach could be circumvented [25], and the second proposing a speci c four-dimensional model with a massive scalar boson [26]. The subsequent paper by Guralnik, Hagen and Kibble [27] referred explicitly to these earlier papers. Also of note is a relatively-unknown 1965 paper by Migdal and Polyakov [28], which discusses the partial breaking of a local non-Abelian symmetry, ahead of the influential paper of Kibble [29].Of all these authors, Higgs was the only one who mentioned explicitly the existence of a massive scalar boson (see equation (2b) of his second paper [26]), and he went on to write a third paper in 1966 [30] that discusses the properties of this `Higgs boson' in surprising detail including, e.g., its decays into massive vector bosons.

John Ellis,Summary of the Nobel Symposium on LHC Results,13/09/2013

**... par l'un de ceux à qui on doit la recherche effective et la découverte du boson de Higgs**

For a decade, very few people took seriously Higgs' prediction of this boson, therebeing only a handful of papers about before the phenomenological pro le that MaryGaillard, Dimitri Nanopoulos and I wrote in 1975 [31]. Fortunately, the LHC communitydid not pay attention to the caveat in the last sentence of our paper that \we do notwant to encourage big experimental searches for the Higgs boson", and the ATLAS andCMS experiments announced the discovery of a candidate for a (the?) Higgs boson onJuly 4th 2012 [32].

ibid.

**Préhistoire du principe de brisure spontanée de symétrie ...**

Landau introduced broken symmetry in condensed matter physics (simultaneously with Tisza...), making the simple observation that a symmetry change, being discrete, implies a thermodynamic phase transition. The higher-temperature and more entropic phase, he assumed, should always be averaging over a larger group and hence be more symmetric, though there are a number of cases where this tendency doesn't work.... I believe it was I who, in 1952, first realised that a massless boson (Goldstone) excitation necesseraly accompanied a broken continuous symmetry, in connection with studying the ground state of an isotropic antiferromagnet. The reason is that the true symmetry must be restored by the zero-point motions, which must therefore have divergent amplitude, hence zero energy. ..It was also Landau (and here his contribution is clear) who introduced the concept of elementary excitations into condensed matter physics. He pointed out that one could consider the ground state of an ordered solid (or quantum fluid) as analogous to the vacuum of a field theory, and the lowest-energy quantum excitations then would be like quanta of a field and could,, at low temperatures, behave like a rarefied gas of elementary particles. Thus he was generalizing Debye and Einstein's phonon theory of the specific heat of a solid. What Nambu did was to be the first to stand on its head Einstein's progression from light as a classical wave in a medium to light as a gas of photons in vacuum to quantized phonon vibrations in a solid; he proposed that the vacuum was not empty space but a condensed phase which broke some symmetry of space-time......the real value of broken symmetry concepts only became apparent when something new and deeply puzzling arrived on the scene. This was the new theory of superconductivity of Bardeen, Cooper and Schrieffer... a lot of discussion revolved around the peculiar fact that although the theory was manifestely neither Galilean nor gauge-invariant, it gave experimental answers which were right on the button....we [Nambu and I] both became "captured by the BCS theory".Both of us realized that the solution to the problem of invariance was the same as it was in other broken symmetry situations: that one has to take into account the zero-point motions of the collective excitations....I think I even learned the words [broken symmetry] from him, if not the idea.But soon he followed it up with something even more radical - the true originof the idea of a dynamical broken symmetry of the vacuum, namely the series of papers with Jona-Lasinio, of which the first was given in April 1960...To me - and I suppose perhaps even more to his fellow particle theorists - this seemed like a fantastic stretch of the imagination. The vacuum ... had at least since Einstein got rid of the aether, been the epitome of emptiness, the space within which the quanta flew about. Momentarily, Dirac had disturbed us with his view of antiparticles as "holes" in a sea, but by redefining the symmetries of the system to include a new symmetry called charge conjugation, we made that seem to go away. I, at least, had my mind encumbered with the idea that if there was a condensate there was something there, with properties like superconductivity that you could measure. I eventually crudely reconciled myself by realizing that if you were observing from inside the superconductor and couldn't see out you wouldn't have anything observable except the spectrum.

Philip W. Anderson,More and Different, 2011

**... par l'un de ces pères fondateurs**

Motivated by his work in condensed matter physics, Philip Anderson showed that spontaneous symmetry breaking of gauge symmetry can give mass to the gauge bosons. His mechanism was essentially a nonrelativistic precursor to the Higgs Mechanism . The work was published in Physics Review rather than a condensed matter journal because Anderson thought it relevant to particle physics. The crucial observation was that the troublesome massless Goldstone boson mode is absorbed into the gauge boson field transforming it from the component field of a massless particle to the three component field of a massive one. He did not point out that a massive scalar boson would also be important.Anderson was overlooked when the 2010 Sakurai prize was given to Higgs, Brout, Englert, Kibble, Guralnik and Hagen for the Higgs mechanism. Some people justify this by pointing out that the relativistic extension of his idea is non-trivial and an important part of the theory. Others say that there is bias against him from particle physicists because he is condensed-matter physicist and argued against funding the American SSC hadron collider. It is a difficult call, he certainly had some of the key elements, but the Nobel Prize is usually only given for more complete theories. In the form presented by Anderson the idea was described by Higgs as crucial but just speculation. At least Higgs cited Anderson’s paper. Brout, Englert, Guralnik, Hagen and Kibble all left the reference out despite being well aware of the prior work.Anderson has the Nobel Prize from 1977 for work on superconductivity.

Philip Gibbs, There is a Nobel Prize for the Higgs Boson, but who will get it?17/05/2012

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