Related papers: (1,9)-spacetime --> (1,3)-spacetime: Reduction => …

In this letter, we introduce a new approach to formulate the family structure of the standard model. Trying to mimic the highly contrained representation structure of the standard model while extending the symmetry, we propose a…

We propose a realistic theory based on the $\mathrm{SU(3)_c \otimes SU(3)_L \otimes SU(3)_R \otimes U(1)_{X}}$ gauge group which requires the number of families to match the number of colors. In the simplest realization neutrino masses…

We give a detailed description of the model construction procedures about our new approach to the family structure of the standard model. SM-like chiral fermion spectra, largely "derivable" from the gauge anomaly constraints, are formulated…

The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the vev and the hypercharge splitting (Delta) of right-handed leptons (quarks) in a family vanish and Q=T_0 + Y independently in each helicity sector. As a…

We discuss a simple and elegant $SU(3)\times SO(10)$ family unified gauge theory in 6d compactified on a torus with the orbifold $T_2/Z_2^3$ and supplemented by a $Z_6\times Z_3$ discrete symmetry. The orbifold boundary conditions generate…

Unification based on the group SO(10)^3 \times S_3 is studied. Each family has its own SO(10) group, and the S_3 permutes the three families and SO(10) factors. This is the maximal local symmetry for the known fermions. Family unification…

If the standard model of quarks and leptons is extended to include three singlet right-handed neutrinos, then the resulting fermion structure admits an infinite number of anomaly-free solutions with just one simple constraint. Well-known…

Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients, isomorphic $\mathcal{G}_{1,4}$. By resorting to matrix representation by means of Dirac-Pauli gamma matrices, the paper…

In this contribution we present the results of a series of investigations of dimensional reduction, applied to SU(3) gauge theory in 2 + 1 dimensions. We review earlier results, present a new reduced model with Z(3) symmetry, and discuss…

We outline our approach to understand the family structure through the idea of a SM-like chiral fermion spectrum, one that is derivable from anomaly cancellation conditions in the same way as the one family SM, under an extended symmetry,…

A simple alternative to the usual Pati-Salam model is proposed. The model allows quarks and leptons to be unified with gauge group $SU(4) \otimes SU(2)_L \otimes SU(2)_R$ at a remarkably low scale of about 1 TeV. Neutrino masses in the…

We consider generalizations of the standard model (SM) which are based on the gauge symmetry $SU(n)_c\otimes SU(m)_L\otimes U(1)_N$. Although the most interesting possibilities occur when $n=3$, we will consider also the cases $n=4,5$ both…

Extending the well-known $SU(3)_C \times SU(3)_L \times SU(3)_R$ model of quarks and leptons to include a fourth $SU(3)_N$ gauge factor, a new realization is obtained, different from leptonic color, which contains a lepton/dark symmetry…

Instead of right-handed neutrino singlets, the standard model is extended to include lepton triplets $(\Sigma^+, \Sigma^0, \Sigma^-)$. Each quark and lepton family may now transform under an anomaly-free $U(1)_X$ gauge symmetry, known…

It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time…

We study the possibility of complete family unification in higher-dimensional space-time. Three families of matters in SU(5) grand unified theory are derived from a single bulk multiplet of SU(N) gauge group (N >= 9) in the framework of…

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…

We discuss extension of the electroweak gauge group to $SU(3)_L \times SU(3)_R \times U(1)_{XL} \times U(1)_{XR}$. This adds new leptons to the familiar 331-model. The explanation for three light quark-lepton families remains but new…

Here we present a candidate for a Z(3)-symmetric reduced action for the description of the (2+1)D SU(3) gauge theory

We study a coset-space unification model for families based on $E_7/SU(5) \times U(1)^3$. We find that qualitative structure of quark and lepton mass matrices in this model describes very well the observation. We stress, in particular, that…