Related papers: Octions: An $E_8$ description of the Standard Mode…

A fermion-boson-type composite model for quarks and leptons is proposed. Elementary fields are only one kind of spin-1/2 and spin-0 preon. Both are in the global supersymmetric pair with the common electric charge of e/6 and belong to the…

We combine $SU(5)$ Grand Unified Theories (GUTs) with $A_4$ modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. Classifying the models according to the…

We examine the phenomenology of a low-energy extension of the Standard Model, based on the gauge group SU(3) x SU(2) x U(1) x SO(3), with SO(3) operating in the shadow sector. This model offers $\nu_{e} \to \nu_{s}$ and $\nu_{\mu} \to…

Grand Unified Theories (GUTs) based on groups like $SO(10)$ and $SU(5)$ unify Standard Model (SM) fermions into irreducible representations (irreps), and predict additional scalar fields beyond the SM Higgs. In $SO(10)$ GUTs, the scalar…

We consider a novel model for three standard families of left chiral states of quarks and leptons conjointly with a new family of dark matter fermionic particles and a sterile neutrino. It is suggested to use a SO(10) symmetry for…

We consider the Standard Model (SM) with the addition of a $\mathrm{U(1)^\prime}$ gauge symmetry and a complete fourth family of quarks and leptons which are vector-like with respect to the full $\mathrm{SU(3)_C}\times \mathrm{SU(2)_L}…

We extend the unitary groups beyond the ${\rm SU}(5)$ and ${\rm SU}(6)$ to look for possible grand unified theories that give rise to three-generational Standard Model fermions without the simple repetition. By demanding asymptotic free…

There are exactly three finite subgroups of SU(2) that act irreducibly in the spin 1 representation, namely the binary tetrahedral, binary octahedral and binary icosahedral groups. In previous papers I have shown how the binary tetrahedral…

In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the…

The supersymmetric flipped $SU(6)\times U(1)$ gauge symmetry can arise through compactification of the ten dimensional $E_8\times E_8$ superstring theory. We show how realistic phenomenology can emerge from this theory by supplementing it…

SO(10), or equivalently its covering group Spin(10), is a well-known promising grand unified group that contains the standard-model group. The spinors of the group Spin($N$) of rotations in $N$ spacetime dimensions are indexed by a bitcode…

A real representation theory of real Clifford algebra has been studied in further detail, especially in connection with Fierz identities. As its application, we have constructed real octonion algebras as well as related octonionic triple…

This paper is a continuation of our works concerning Linear Canonical Transformations (LCT) and Phase Space Representation of Quantum Theory. The purpose is to study the spinorial representation of some particular LCT called Isodispersion…

Postulating that spacetime is discrete, we assume that physical space is described by a 3-dimensional cubic lattice.The corresponding symmetry group of rotations has order 24 and motivates the introduction of a cubic shaped graph with 27…

We describe a remarkable rank fourtenn matrix factorization of the octic Spin(14)-invariant polynomial on either of its half-spin representations. We observe that this representation can be, in a suitable sense, identified with a tensor…

This paper represents a first attempt at unifying two promising models that attempt to explain the origin of the internal symmetries of leptons and quarks. It is shown that each of the four normed division algebras over the reals admits a…

We construct a compactification of the heterotic string on an orbifold T^6/Z_6 leading to the standard model spectrum plus vector--like matter. The standard model gauge group is obtained as an intersection of three SO(10) subgroups of E_8.…

We review the possibility that the Supersymmetric Standard Model arises from orbifold constructions of the E_8 x E_8 Heterotic Superstring, and the phenomenological properties that such a model should have. In particular, trying to solve…

The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to…

We embed the flipped SU(5) models into the SO(10) models. After the SO(10) gauge symmetry is broken down to the flipped SU(5) \times U(1)_X gauge symmetry, we can split the five/one-plets and ten-plets in the spinor \mathbf{16} and…