A Grand Unified Theory, ( GUT ), is a model in particle physics in which at high energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry and thus one unified coupling constant.

They would also cause extremely rapid proton decay ( far below current experimental limits ) and prevent the gauge coupling strengths from running together in the renormalization group.

A GUT model basically consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a Yang-Mills action for that connection given by an invariant symmetric bilinear form over its Lie algebra ( which is specified by a coupling constant for each factor ), a Higgs sector consisting of a number of scalar fields taking on values within real / complex representations of the Lie group and chiral Weyl fermions taking on values within a complex rep of the Lie group.

This interesting numerical observation is called the gauge coupling unification, and it works particularly well if one assumes the existence of superpartners of the Standard Model particles.

* In the electroweak theory unifying the weak interaction with electromagnetism, α is absorbed into two other coupling constants associated with the electroweak gauge fields.

One piece of evidence for supersymmetry existing is gauge coupling unification.

The renormalization group evolution of the three gauge coupling constants of the Standard Model is somewhat sensitive to the present particle content of the theory.

Continuing the analogy with QCD, the running gauge coupling α < sub > TC </ sub >( μ ) triggers spontaneous chiral symmetry breaking, the technifermions acquire a dynamical mass, and a number of massless Goldstone bosons result.

This coupling is induced by gauge bosons of the enlarged group.

In 1986 Appelquist, Karabali and Wijewardhana discussed the enhancement of fermion masses in an asymptotically free technicolor theory with a slowly running, or “ walking ”, gauge coupling.

For this special choice of chiral matter, the vacuum expectation values of the matter scalar fields can be chosen to completely break the gauge symmetry at weak coupling, allowing a reliable semi-classical saddle point calculation to proceed.

* If we have a charge symmetry, that symmetry has to be a gauge symmetry, not a global one, and in the spectrum of charged particles, there has to be at least a particle with a mass in Planck units less than the gauge coupling strength.

where is the color gauge coupling ( which is a function of and associated with asymptotic freedom ) and is the Yukawa coupling.

This can be easily realized when we look at the coupling between the gauge field and the ghost field that is.

In a non-Abelian gauge theory, the gauge coupling parameter,, appears in the Lagrangian as

The design was further modified for use on Melbourne's broad gauge track, and its control system was designed specifically to allow in-service coupling and operation with Comeng sets.

In addition to mediating proton decay, they alter gauge coupling unification.

If one adds a suitable gravitational term to the standard model action with gravitational coupling, the theory becomes locally scale invariant ( i. e. Weyl invariant ) in the unitary gauge for the local SU ( 2 ).

The main idea behind the little Higgs models is that the one-loop contribution to the tachyonic Higgs boson mass coming from the top quark cancels ( the other one-loop contributions are small enough that they don't really matter ; the top Yukawa coupling is huge ( because related to its mass ) and all the other Yukawa couplings and gauge couplings are small ).

for a given gauge field ( here we use ), with gauge coupling constant g. The quantity is the structure constant of the particular gauge group, defined by the commutator, where are the generators of the group.

The magnetic charges of a gauge field theory can be understood to be the group generators of the cohomology group for the fiber bundle M. The cohomology arises from the idea of classifying all possible gauge field strengths, which are manifestly exact forms, modulo all possible gauge transformations, given that the field strength F must be a closed form:.

Although one can compute the field strengths explicitly in the Coulomb gauge and demonstrate that changes in them propagate at the speed of light, it is much simpler to observe that the field strengths are unchanged under gauge transformations and to demonstrate causality in the manifestly Lorentz covariant Lorenz gauge described below.

In technical terms, they are vector gauge bosons that mediate strong interactions of quarks in quantum chromodynamics ( QCD ).

In 1972 he and Harald Fritzsch introduced the conserved quantum number " color charge ", and later along with Heinrich Leutwyler, they introduced quantum chromodynamics ( QCD ) as the gauge theory of the strong interaction ( cf.

QCD is a quantum field theory of a special kind called a non-abelian gauge theory, consisting of a ' color field ' mediated by a set of exchange particles ( the gluons ).

QCD is a gauge theory of the SU ( 3 ) gauge group obtained by taking the color charge to define a local symmetry.

They are emergent gauge bosons in an approximate string description of QCD.

The gauge invariant QCD Lagrangian is

This loop variable plays a most-important role in discretized forms of the QCD ( see lattice QCD ), and more generally, it distinguishes confined and deconfined states of a gauge theory.

In contrast, in the QCD they " fluctuate " ( annealing ), and through the large number of gauge degrees of freedom the entropy plays an important role ( see below ).

Mathematically, QCD is a non-Abelian gauge theory based on a local ( gauge ) symmetry group called SU ( 3 ).

In QCD the gauge group is the non-abelian group SU ( 3 ).

Much technicolor research focuses on exploring strongly-interacting gauge theories other than QCD, in order to evade some of these challenges.

They extended their calculation to SU ( 2 ) gauge theories with fundamental matter in Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD.

After his PhD, he became interested in the role of gauge theories in the strong interaction, the leading theory of which is called quantum chromodynamics or QCD.

In non-abelian gauge theories such as QCD, the existence of asymptotic freedom depends on the gauge group and number of flavors of interacting particles.

For SU ( 3 ), the color charge gauge group of QCD, the theory is therefore asymptotically free if there are 16 or fewer flavors of quarks.

In the most commonly-considered cases, such as lattice QCD, fermion fields are defined at lattice sites ( which leads to fermion doubling ), while the gauge fields are defined on the links.

Monte Carlo methods are free from the sign problem when applied to the case of QCD with gauge group SU ( 2 ) ( QC < sub > 2 </ sub > D ).

While the gauge group of QCD is, we can generalize to any number of colors,, with gauge group.

The corresponding gauge bosons are the three W bosons of weak isospin from SU ( 2 ) (,, and ), and the B < sup > 0 </ sup > boson of weak hypercharge from U ( 1 ), respectively, all of which are massless.

While the description of strong and weak interactions within the Standard Model is based on gauge symmetries governed by the simple symmetry groups SU ( 3 ) and SU ( 2 ) which allow only discrete charges, the remaining component, the weak hypercharge interaction is described by an abelian symmetry U ( 1 ) which in principle allows for arbitrary charge assignments.

He had apparently overlooked the effects of minimum gauge, and simply scaling up the original small models resulted in a design that was too weak to hold itself together.

The force carrier particles that mediate the electromagnetic, strong, and weak interactions are called gauge bosons.

* Twelve gauge bosons ( force carriers ): the photon of electromagnetism, the three W and Z bosons of the weak force, and the eight gluons of the strong force ;

The discovery of the weak gauge bosons through the 1980s, and the verification of their properties through the 1990s is considered to be an age of consolidation in particle physics.

The importance of gauge theories for physics stems from their tremendous success in providing a unified framework to describe the quantum-mechanical behavior of electromagnetism, the weak force and the strong force.

The strong, weak, and electromagnetic forces can all be understood as arising from gauge symmetries.

The Standard Model incorporates parity violation by expressing the weak interaction as a chiral gauge interaction.

The combination of the SU ( 2 ) gauge theory of the weak interaction, the electromagnetic interaction, and the Higgs mechanism is known as the Glashow-Weinberg-Salam model.

The Standard Model of particle physics recognizes three kinds of gauge bosons: Photons, which carry the electromagnetic interaction ; W and Z bosons, which carry the weak interaction ; and gluons, which carry the strong interaction.

In the Standard Model, the phrase " Higgs mechanism " refers specifically to the generation of masses for the W < sup >±</ sup >, and Z weak gauge bosons through electroweak symmetry breaking.

The vector bosons considered to be elementary particles in the Standard Model are the gauge bosons or, the force carriers of fundamental interactions: the photon of electromagnetism, the W and Z bosons of the weak interaction, and the gluon of the strong interaction.

* The bino is the superpartner of the U ( 1 ) gauge field corresponding to weak hypercharge.

The Higgsino is a Dirac fermion and that is a weak isodoublet with hypercharge half under the Standard Model gauge symmetries.

A U-shaped clincher rim must be made of relatively heavier gauge material to prevent the tire pressure from spreading the inherently weak U shape and allowing the tire to come off the rim.

On the theoretical front, gauge theories with broken symmetry became the first fully viable contenders for explaining the weak interaction after Gerardus't Hooft discovered in 1971 how to calculate with them beyond tree level.

All its fermions are chiral Weyl fermions, which means that the weak gauge bosons only couple to left-handed quarks and leptons.