Related papers: Six Bits
The assumption that space-time is a noncommutative space formed as a product of a continuous four dimensional manifold times a finite space predicts, almost uniquely, the Standard Model with all its fermions, gauge fields, Higgs field and…
We propose a simple non-supersymmetric grand unified theory (GUT) based on the gauge group $SO(10) \times U(1)_\psi$. The model includes 3 generations of fermions in ${\bf 16}$ ($+1$), ${\bf 10}$ ($-2$) and ${\bf 1}$ ($+4$) representations.…
The observed replication of fermions in three families is undoubtedly a reflection of a deeper symmetry underlying the standard model. In this paper we investigate one very elementary possibility, that physics above the grand unification…
A field model of two-component fermions is described, the consequences of which coincide in the main with primary postulates of the standard model. Such a model can be constructed for 4 generations at the minimum. Peculiarities of the…
We review the role in physics of the Pin groups, double covers of the full Lorentz group. Pin(1,3) is to O(1,3) what Spin(1,3) is to SO(1,3). The existence of two Pin groups offers a classification of fermions based on their properties…
In a space of $d=15 $ Grassmann coordinates, two types of generators of the Lorentz transformations, one of spinorial and the other of vectorial character, both linear operators in Grassmann space, forming the group $ SO(1,14) $ which…
The Sine-Gordon theory at $\frac{\beta^{2}}{8\pi} = \frac{2}{(2n+3)},\; n= 1,2,3 \cdots $ has a higher spin generalization of the $N=2$ supersymmetry with the central terms which arises from the affine quantum group $U_{q}( \hat{s \ell}…
It is a commonplace that any theory can be written in any coordinates via tensor calculus. But it is claimed that spinors as such cannot be represented in coordinates in a curved space-time. What general covariance means for theories with…
I show how the symmetry-breaking of a recently proposed embedding of the standard model of particle physics in $E_8$ can be explained in terms of the representation theory of the binary tetrahedral group. This finite group provides a link…
We construct renormalizable Standard Model extensions, valid up to the Planck scale, that give a composite Higgs from a new fundamental strong force acting on fermions and scalars. Yukawa interactions of these particles with Standard Model…
I present a modified version of the Manogue-Dray-Wilson `octions' model of elementary particles, that overcomes some of the objections to that model that have been raised. In particular, I restore the compactness of the Standard Model gauge…
Expanding the results of [1], [2], [3], we demonstrate a network of algebraic connections between six well-known particle theories. These are the Spin(10) model, the Georgi-Glashow model, the Pati-Salam model, the Left-Right Symmetric…
Fifty years ago the {\it standard model} offered an elegant new step towards understanding elementary fermion and boson fields, making several assumptions, suggested by experiments. The assumptions are still waiting for an explanation.…
The Atiyah-Singer index theorem is investigated on various compact manifolds which admit finite matrix approximations (``fuzzy spaces'') with a view to applications in a modified Kaluza-Klein type approach in which the internal space…
Following up on our earlier work where we showed how to amend a scheme originally proposed by M. Gell-Mann to identify the 48 spin 1/2 fermions of N=8 supergravity that remain after complete breaking of N=8 supersymmetry with the 3x16…
We propose a minimal SO(10) model in 5 space-time dimensions. The single extra spatial dimension is compactified on the orbifold S^1/(Z_2 x Z_2') reducing the gauge group to that of Pati-Salam. The breaking down to the standard model group…
The spin-charge-family theory, which is a kind of the Kaluza-Klein theories in $d=(13+1)$ --- but with the two kinds of the spin connection fields, the gauge fields of the two Clifford algebra objects, $S^{ab}$ and $\tilde{S}^{ab}$ ---…
In a scheme originally proposed by M. Gell-Mann, and subsequently shown to be realized at the SU(3)xU(1) stationary point of maximal gauged SO(8) supergravity by N. Warner and one of the present authors, the 48 spin 1/2 fermions of the…
An analytic computation is given of the generation of Yukawa couplings and of the quark, charged lepton and neutrino masses in the framework of an SO(10) model with a unified Higgs sector consisting of a single pair of vector-spinor $144 +…
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: * the standard Higgs scalar…