In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, they would merge into a single force. Thus, if the universe is hot enough (approximately 1015 K, a temperature not believed to have been exceeded since shortly after the Big Bang), then the electromagnetic force and weak force merge into a combined electroweak force. During the quark epoch, the electroweak force split into the electromagnetic and weak force. (For comparison, the current hottest man-made temperature is slightly higher than 1012 K.)
A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this unified force has not been directly observed, many GUT models theorize its existence. If unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.
In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×1034 years.
In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos. It appears in the plane-wave solution to the Dirac equation, and is a certain combination of two Weyl spinors, specifically, a bispinor that transforms "spinorially" under the action of the Lorentz group.
In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras , all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6. The designation E6 comes from the Cartan–Killing classification of the complex simple Lie algebras (see Élie Cartan § Work). This classifies Lie algebras into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E6 algebra is thus one of the five exceptional cases.
In particle physics, the Georgi–Glashow model is a particular grand unified theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. In this model the standard model gauge groups SU(3) × SU(2) × U(1) are combined into a single simple gauge group SU(5). The unified group SU(5) is then thought to be spontaneously broken into the standard model subgroup below a very high energy scale called the grand unification scale.
In physics, the Pati–Salam model is a Grand Unified Theory (GUT) proposed in 1974 by Abdus Salam and Jogesh Pati. Like other GUTs, its goal is to explain the seeming arbitrariness and complexity of the Standard Model in terms of a simpler, more fundamental theory that unifies what are in the Standard Model disparate particles and forces. The Pati–Salam unification is based on there being four quark color charges, dubbed red, green, blue and violet, instead of the conventional three, with the new "violet" quark being identified with the leptons. The model also has left–right symmetry and predicts the existence of a high energy right handed weak interaction with heavy W' and Z' bosons and right-handed neutrinos.
The Flipped SU(5) model is a grand unified theory (GUT) first contemplated by Stephen Barr in 1982, and by Dimitri Nanopoulos and others in 1984. Ignatios Antoniadis, John Ellis, John Hagelin, and Dimitri Nanopoulos developed the supersymmetric flipped SU(5), derived from the deeper-level superstring.
In physics, the trinification model is a Grand Unified Theory proposed by Alvaro De Rújula, Howard Georgi and Sheldon Glashow in 1984.
In mathematics the spin group Spin(n) is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups
The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers only "the [minimum] number of new particle states and new interactions consistent with phenomenology". Supersymmetry pairs bosons with fermions, so every Standard Model particle has a superpartner yet undiscovered. If discovered, such superparticles could be candidates for dark matter, and could provide evidence for grand unification or the viability of string theory. The failure to find evidence for MSSM using the Large Hadron Collider has strengthened an inclination to abandon it.
In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras, and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing the Poincaré algebra, and the odd part is built from spinors on which there is an anticommutation relation with values in the even part.
A chiral phenomenon is one that is not identical to its mirror image. The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry.
In particle physics, the doublet–triplet (splitting) problem is a problem of some Grand Unified Theories, such as SU(5), SO(10), and . Grand unified theories predict Higgs bosons arise from representations of the unified group that contain other states, in particular, states that are triplets of color. The primary problem with these color triplet Higgs is that they can mediate proton decay in supersymmetric theories that are only suppressed by two powers of GUT scale. In addition to mediating proton decay, they alter gauge coupling unification. The doublet–triplet problem is the question 'what keeps the doublets light while the triplets are heavy?'
In particle physics, SO(10) refers to a grand unified theory (GUT) based on the spin group Spin(10). The shortened name SO(10) is conventional among physicists, and derives from the Lie algebra or less precisely the Lie group of SO(10), which is a special orthogonal group that is double covered by Spin(10).
This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.
In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion.
The Gross–Neveu (GN) model is a quantum field theory model of Dirac fermions interacting via four fermion interactions in 1 spatial and 1 time dimension. It was introduced in 1974 by David Gross and André Neveu as a toy model for quantum chromodynamics (QCD), the theory of strong interactions. It shares several features of the QCD: GN theory is asymptotically free thus at strong coupling the strength of the interaction gets weaker and the corresponding function of the interaction coupling is negative, the theory has a dynamical mass generation mechanism with chiral symmetry breaking, and in the large number of flavor limit, GN theory behaves as t'Hooft's large limit in QCD.
In lattice field theory, staggered fermions are a fermion discretization that reduces the number of fermion doublers from sixteen to four. They are one of the fastest lattice fermions when it comes to simulations and they also possess some nice features such as a remnant chiral symmetry, making them very popular in lattice QCD calculations. Staggered fermions were first formulated by John Kogut and Leonard Susskind in 1975 and were later found to be equivalent to the discretized version of the Dirac–Kähler fermion.
In particle physics, the X and Y bosons are hypothetical elementary particles analogous to the W and Z bosons, but corresponding to a unified force predicted by the Georgi–Glashow model, a grand unified theory (GUT).
