T he shunning of Denis Mukwege in favour of chemical weapon destroyers in Syria in the Nobel peace stakes was yesterday's curiosity. But physics and chemistry Nobels often reward endeavours that began as pure curiosity. The shorthand is "blue skies research", work with no obvious practical application and no pot of gold at the end of the rainbow. In there was a proposal that matter, space and time may have pecked out of some kind of cosmic egg, and a counter-proposal that the universe was eternal and looked to be expanding only because matter was constantly being created. For most people, both arguments had no more substance than fairy tales: there was no evidence. Almost 50 years on, Cern's Large Hadron Collider has more or less produced an answer to the question about why matter has mass.

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Curator: Tom W B Kibble. Eugene M. Nicolau Leal Werneck. The Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism provides the means by which gauge vector bosons can acquire nonzero masses in the process of spontaneous symmetry breaking. It is a key element of the electroweak theory that forms part of the standard model of particle physics, and of many models, such as Grand Unified Theories, that go beyond it.

The discovery of the Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism effectively removed a major obstacle to constructing a unified theory of weak and electromagnetic interactions. Initially, invoking spontaneous symmetry breaking was thought to introduce yet another problem, the appearance of the massless scalar Nambu-Goldstone bosons , as seemingly required by the Goldstone theorem for reasons explained below.

It turns out, however, that these two problems in a sense "cancel out". The mechanism is essentially a relativistic version of one that operates in a superconductor. The history of the development of the idea is discussed in the article Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism history. Spontaneous symmetry breaking occurs when the ground state of a system does not share the full symmetry of the underlying theory.

This assumption is important for reasons explained below. The direction in which they point is arbitrary. Thus there is a degenerate ground state. Making a simultaneous rotation of all the spins yields another ground state, with exactly the same energy see Figure 2 b. A very important consequence of spontaneous symmetry breaking of a continuous symmetry like this one is that there are excitations whose energy goes to zero in the long wavelength limit.

These are the Goldstone bosons or Nambu-Goldstone bosons. In this case these are spin waves, in which a periodic space-dependent rotation is applied to the spins see Figure 2 c.

Since it costs no energy to rotate all the spins, from a to b , it costs very little energy to make a long-wavelength periodic change.

This is the content of the Goldstone theorem. For a ferromagnet, the symmetry is broken even in finite volume. For the Goldstone model, the situation is different. But this is not the case for a field theory in infinite volume.

Note that the representation of the canonical commutation relations on this Hilbert space is inequivalent to the usual Fock-space representation -- in contrast to the situation in ordinary quantum mechanics where all irreducible representations of the Heisenberg commutation relations are unitarily equivalent. Nambu-Goldstone bosons appear here too. The first term here is merely an unimportant constant. Their presence is required by the Goldstone theorem in any manifestly Lorentz covariant theory in which a continuous symmetry is spontaneously broken.

The theorem is also true for non-relativistic theories, provided that an additional assumption is satisfied. This is discussed further below. This is the simplest of all gauge theories , with an Abelian U 1 gauge group. Now, however, there are additional quadratic terms arising from the first, kinetic term in It is now clear that the second term gives the gauge field a mass.

How was it possible to arrive at a theory with no massless particles, despite the Goldstone theorem which might seem to demand their presence? To answer this question it may be helpful to start by examining one of the proofs of Goldstone's theorem. It is based on three hypotheses. Secondly, this symmetry is spontaneously broken; there is no invariant vacuum state, but rather a degenerate family of non-invariant vacuum states.

It follows from Eqs. The key lies in the third hypothesis, of manifest covariance. To quantize a gauge theory, one must choose a gauge, and impose a gauge-fixing condition of some kind. For the U 1 gauge theory, if one wants a formulation in terms of a Hilbert space containing only physical states, this cannot be done in a manifestly covariant way.

In this case, commutators are not required to vanish outside the light cone, and in fact fall off only like an inverse power. Here the Goldstone theorem definitely does apply, and there do exist massless Nambu-Goldstone bosons.

But it turns out that they are purely gauge modes, uncoupled to the physical particles of the theory. This mechanism is often said to exhibit "spontaneously broken gauge symmetry".

That is a convenient shorthand description, but the terminology is potentially somewhat misleading. The process of quantization requires a choice of gauge, i. It is, however, very important that the model derives from an initial fully gauge-invariant one. In general, models involving massive vector fields are non-renormalizable.

But this theory is renormalizable, as proved by 't Hooft see gauge theories , primarily because it retains the Ward identities that play a key role in the renormalizability of quantum electrodynamics. Essentially the same mechanism can apply in the case of a non-Abelian gauge theory.

Other points on the sphere will correspond to other vacua. In this case, the symmetry group SO 3 is not broken completely. The primary purpose of the Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism was to provide masses for the gauge vector bosons.

A secondary effect, however, was to give masses to other fundamental particles. It is sometimes said that the Higgs field gives masses to all other particles, but that is not strictly correct. It is important to note that most of the mass of the nucleon in particular does not arise in this way. The larger part of the nucleon mass comes from a mechanism along the lines sketched out earlier by Nambu see Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism history.

Editor's note: The title of this article has been chosen by the editor on the basis of the principle of maximal or so historical fairness and on the basis of a talk given by Steven Weinberg at BCS 50, held on 10—13 October at the University of Illinois at Urbana—Champaign to celebrate the 50th anniversary of the BCS paper. The order of the three groups of authors reflects the historical order in which Physics Review Letter received and published the corresponding articles in its volume 13 RG, Editor of the Encyclopedia of Physics.

Tom W B Kibble , Scholarpedia, 4 1 Jump to: navigation , search. Chris Quigg. John C Taylor. Sponsored by: Eugene M. Izhikevich , Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia Sponsored by: Dr. Namespaces Page Discussion. Views Read View source View history. Contents 1 Role of the mechanism 2 Spontaneous symmetry breaking 2. Izhikevich , Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia. Sponsored by: Dr. Reviewed by : Prof. Accepted on: GMT.

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## Nobel prizes: curiouser and curiouser

In the Standard Model of particle physics , the Higgs mechanism is essential to explain the generation mechanism of the property " mass " for gauge bosons. The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field the Higgs field that permeates all space to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass.

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## Higgs mechanism

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