Related papers: A note on the Lipkin model in arbitrary fermion nu…
A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $ H=\omega J_{3}+\alpha J_{-}+\beta J_{+}$, $\alpha \neq \beta$, is analyzed. The metrics which…
Massive neutrinos are a generic prediction of SO(10), and models of unification cry for supersymmetry. Since we have a rather detailed information on neutrino and charged fermion masses, the real question is: how/whether it is possible to…
We show that under a new U(1) gauge symmetry, which is non-anomalous in the presence of one ``right-handed neutrino'' per generation and consistent with the standard model Yukawa couplings, the most general fermion charges are determined in…
Recently it was demonstrated that free fermionic heterotic-strings can produce models with solely the Minimal Supersymmetric Standard Model states in the low energy spectrum. This unprecedented result provides further strong evidence for…
With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in…
We consider nonlinear, scaling-invariant N=1 boson + fermion supersymmetric systems whose right-hand sides are homogeneous differential polynomials and satisfy some natural assumptions. We select the super-systems that admit infinitely many…
We construct and analyze nonsupersymmetric SO(10) standard model extensions which explain dark matter (DM) through the fermionic Higgs portal. In these SO(10)-based models the DM particle is naturally stable since a $Z_2$ discrete symmetry,…
We construct large classes of exactly solvable pseudo-Hermitian 2D spin Hamiltonians. The ground states of these systems depend only on the spatial topology of the system. We identify the ground state system on a surface with the value…
We propose a model based on the $SU(5)$ grand unification with an extra $Z_{2}\otimes Z_{2}^{\prime}\otimes Z_{2}^{\prime \prime}\otimes Z_{4}\otimes Z_{12}$ flavor symmetry, which successfully describes the observed SM fermion mass and…
We describe non-relativistic fermions on the lattice (Hubbard model) in the canonical formulation using transfer matrices in fixed fermion number sectors such that the partition function becomes fully factorized in time. By analytically…
In the context of SU(3)_c x SU(2)_L x [U(1)]^n, SU(3)_c x SU(2)_L x SU(2)_R x [U(1)]^n' and SU(3)_c x SU(3)_L x[U(1)]^n'', we analyze the possible values for n, n' and n''. That is, we look for the number of family-independent, independent…
We consider an extension of the real Lie algebra $\mathfrak{su}(2)$ by introducing a parity operator $P$ and a parameter $c$. This extended algebra is isomorphic to the Bannai-Ito algebra with two parameters equal to zero. For this algebra…
We propose a simple supersymmetric SO(10) GUT model with only doublet Higgs scalars. The fermion mass problem is naturally solved by a new one-loop diagram. R-parity is conserved implying a stable LSP which can explain the dark matter of…
Concerning the su(2)-Lipkin model, the calculation of the excitation energy to the 1st excited-state gives rise to the following fact: The two results based on the exact treatment and the conventional random phase approximation (RPA) are in…
We show how to classify the asymptotically-free gauge theories in four spacetime dimensions, focussing here on the case of purely fermionic matter. The classification depends on the fact (which we prove) that both the dimension and Dynkin…
We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using…
For the particular class of \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} electro-weak models without exotic electric charges, some plausible phenomenological predictions - such as the boson mass spectrum and charges of all the fermions involved…
In recent work arXiv:1412.1715 it was shown how to modify Gell-Mann's proposal for identifying the 48 quarks and leptons of the Standard Model with the 48 spin-1/2 fermions of maximal SO(8) gauged supergravity that remain after the removal…
A complete set of fermion and Higgs superfields is introduced with well-defined SO(10) properties and U(1) x Z_2 x Z_2 family charges from which the Higgs and Yukawa superpotentials are constructed. The structures derived for the four Dirac…
A full account is given of the procedure used by the authors to construct an SO(10) supersymmetric grand unified model of the fermion mass matrices. Various features of the model which gives remarkably accurate results for the quark and…