Types of quantum field thories
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.
There is no lack of proposals for realizing the Higgs field in various big schemes of mathematical structures modelling physics.
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.
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).
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.
|gravity||electroweak and strong nuclear force||fermionic matter||scalar field|
|field content:||vielbein field||principal connection||spinor||scalar field|
|Lagrangian:||scalar curvature density||field strength squared||Dirac operator component density||field strength squared + potential density|
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)
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