# Contents

## Idea

The Higgs field or Higgs boson is a scalar physical field/fundamental particle in a gauge theory such as the standard model of particle physics supposedly responsible for the spontaneously broken symmetry of the electroweak field (electroweak symmetry breaking) and for giving elementary particles their masses by the Higgs mechanism.

## Models

There is no lack of proposals for realizing the Higgs field in various big schemes of mathematical structures modelling physics.

For instance

• in the technicolor model the Higgs field is not a fundamental particle but a compound of fermions. This realizes the Higgs effect entirely in ordinary gauge theory;

• in string theory (see string phenomenology) a Higgs can arise in all sorts of ways. Notably in “intersecting brane models” it arises from strings localized at intersecting points (for a typical kind of survey see for instance around slide 33 here)

• in noncommutative geometry it has been shown that the Higgs may be modeled as a component of the gauge bosons assuming that the KK-reduction is over a certain non-commutative space of classical dimension 0.

## History

The Higgs mechanism was proposed in 1963-1964 by a fair number of authors essentially simultaneously, see the References below. The explicit prediction of the Higgs boson implied by this mechanism though seems to be solely due to (Higgs 64).

The Higgs boson (or at least something very much like it) was finally detected in 2013 at the LHC experiment.

So for the Higgs particle prediction and experimental detection lie apart by about 50 years. Compare maybe to the neutrino, which was predicted in 1930 and detected in 1956, about 26 years later.

standard model of particle physics and cosmology

theory:Einstein-Yang-Mills-Dirac-Higgs
gravityelectroweak and strong nuclear forcefermionic matterscalar field
field content:vielbein field $e$principal connection $\nabla$spinor $\psi$scalar field $H$
Lagrangian:scalar curvature densityfield strength squaredDirac operator component densityfield strength squared + potential density
$L =$$R(e) vol(e) +$$\langle F_\nabla \wedge \star_e F_\nabla\rangle +$$(\psi , D_{(e,\nabla)} \psi) vol(e) +$$\nabla \bar H \wedge \star_e \nabla H + \left(\lambda {\vert H\vert}^4 - \mu^2 {\vert H\vert}^2 \right) vol(e)$

## References

The original articles explaining what is now called the Higgs mechanism by spontaneous symmetry breaking were

• P. Anderson, Plasmons, gauge invariance and mass, Physical Review 130: 439. (1963)

• François Englert, Robert Brout, Broken Symmetry and the Mass of Gauge Vector Mesons, Physical Review Letters 13 (9): 321–23. (1964)

• Gerald Guralnik, C. R. Hagen, ; T. W. B. Kibble, Global Conservation Laws and Massless Particles Physical Review (1964)

• Peter Higgs, Broken Symmetries and the Masses of Gauge Bosons, Physical Review Letters 13 (16): 508–509. (1964)

While all these articles essentially describe the Higgs mechanism, appearently only the one by Peter Higgs explicitly points out that this mechanism predicts the existence of a new, then unobserved, boson, the one therefore now called the Higgs boson.

The general theory of spontaneous symmetry breaking is reviewed in

• Jeremy Bernstein, Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that, Rev. Mod. Phys. 46, 7–48 (1974) (pdf)

The phenomenology of Higgs models is discussed in

• Marcela Carena, Howard E. Haber, Higgs Boson Theory and Phenomenology, Prog.Part.Nucl.Phys.50:63-152,2003 (arXiv:hep-ph/0208209)

Revised on July 1, 2014 03:18:09 by Urs Schreiber (89.204.138.13)