# 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 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.

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=$$R\left(e\right)\mathrm{vol}\left(e\right)+$$⟨{F}_{\nabla }\wedge {\star }_{e}{F}_{\nabla }⟩+$$\left(\psi ,{D}_{\left(e,\nabla \right)}\psi \right)\mathrm{vol}\left(e\right)+$$\nabla \overline{H}\wedge {\star }_{e}\nabla H+\left(\lambda {\mid H\mid }^{4}-{\mu }^{2}{\mid H\mid }^{2}\right)\mathrm{vol}\left(e\right)$

## References

The general theory of spontaneous symmetry breaking is discussed 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 January 14, 2013 18:23:36 by Urs Schreiber (203.116.137.162)