Related papers: Octions: An $E_8$ description of the Standard Mode…
An extension of the Standard Model to the local gauge group SU(3)_c X SU(3)_L X U(1)_X as a family independent model is presented. The mass scales, the gauge boson masses and the masses for the spin 1/2 particles in the model are studied.…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
A possible connection between the existence of three quark-lepton generations and the triality property of SO(8) group (the equality between 8-dimensional vectors and spinors) is investigated.
We present a minimal non-supersymmetric SO(10) GUT breaking directly to the Standard Model gauge group. Precise gauge coupling unification is achieved due to the presence of two color-octet scalars, one of which is accessible to LHC…
In this paper we reconsider, for N=8 supergravity, the problem of gauging the most general electric subgroup. We show that admissible theories are fully characterized by a single algebraic equation to be satisfied by the embedding of the…
In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this condition can be described by Hermitian matrices over the complexes…
We discuss the common features between the Standard Model taxonomy of particles, based on electric charge, strangeness and isospin, and the taxonomy emerging from the key structural elements of the rotating neutrino model, which describes…
We give a model for composite quarks and leptons based on the semisimple gauge group SU(4), with the preons in the 10 representation; this choice of gauge gluon and preon multiplets is motivated by the possibility of embedding them in an…
Lambek's unified classification of the elementary interaction-quanta of the ``Standard model'' is formulated in terms of the 24 units of the integer-quaternion ring, i.e., the tetrahedral group Q_{24}. An extension of Lambek's scheme to the…
In continuation of our model of composite electron, its companion neutrinos, photon and electro-weak gauge bosons as well as their super-partners based on extended Lorentz group $SU(3)\otimes SU(3)$ in (8+1) dimensional space-time, we show…
These four lectures constitute a gentle introduction to what may lie beyond the standard model of quarks and leptons interacting through $SU(3)_c \otimes SU(2)_L \otimes U(1)_Y$ gauge bosons, prepared for an audience of graduate students in…
In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$…
We conjecture how the particle content of the standard model can emerge starting with a supersymmetric Wess-Zumino model in 1+1 dimensions (d = 2) with three real boson and fermion fields. Considering SU(3) transformations, the lagrangian…
Standard Model may be defined with the additional discrete symmetry, i.e. with the gauge group $SU(3)\times SU(2) \times U(1)/{\cal Z}$ (${\cal Z} = Z_6$, $Z_3$ or $Z_2$) instead of the usual $SU(3)\times SU(2) \times U(1)$. It has the same…
In grand unified theories with gauge groups larger than SU(5), the multiplets that contain the known quarks and leptons also contain fermions that are singlets under the Standard Model gauge group. Some of these could be the dark matter of…
The Standard Model group and matter spectrum is obtained in vacua of F-theory, without resorting to an intermediate unification group. The group SU(3) x SU(2) x U(1)_Y is the commutant to SU(5)_t \times U(1)_Y structure group of a Higgs…
Motivated by the simplicity and direct phenomenological applicability of field-theoretic orbifold constructions in the context of grand unification, we set out to survey the immensely rich group-theoretical possibilities open to this type…
A recent series of works by M. Dubois-Violette, I. Todorov and S. Drenska characterised the SM gauge group GSM as the subgroup of SO(9) that, in the octonionic model of the later, preserves the split O=C+C3 of the space of octonions into a…
We explicitly construct a particular real form of the Lie algebra $\mathfrak{e}_7$ in terms of symplectic matrices over the octonions, thus justifying the identifications $\mathfrak{e}_7\cong\mathfrak{sp}(6,\mathbb{O})$ and, at the group…
We desribe in detail a Z_6 orbifold compactification of the heterotic E_8 x E_8 string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), two of…