Related papers: Quantum number conservation in intergenerational i…
We present the characterizations of symbol correspondences for mechanical systems that are symmetric by $SU(3)$, which we refer to as \emph{quark systems}. The quantum quark systems are the unitary irreducible representations of $SU(3)$ of…
We introduce an effort to catalog the gauge-invariant interactions of Standard Model (SM) particles and new fields in a variety of representations of the SM color gauge group $\text{SU}(3)_{\text{c}}$. In this first installment, we direct…
In a scenario in which fourth generation fermions exist, we study effects of new physics on the differential decay width, forward-backward asymmetry $A_{\text{FB}}$ and integrated branching ratio for $B\to X_s \ell^+ \ell^-$ decay with…
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…
Mass matrix of quarks is studied in the Supersymmetric $E_6$ Grand Unified Theory (GUT). The fundamental representation $\textbf{27}$ in $E_6$ which corresponds to one generation contains two sets of $\textbf{5}^{*}$'s in SU(5), so that…
We discuss the quantum state structure using the standard model for three colored quarks in the fundamental representations of $SU(3)_c$ making up the singlet ground state of the hadrons. This allows us to calculate a finite von Neumann…
We describe a quantum error-detecting and error-correcting code embedded within irreducible representations of SU(3). These logical qutrits inherit the He(3) symmetries induced by the representation, while protecting against small SU(3)…
We continue the study undertaken in [13] of the relevance of the exceptional Jordan algebra $J^8_3$ of hermitian $3\times 3$ octonionic matrices for the description of the internal space of the fundamental fermions of the Standard Model…
We propose a supersymmetric technicolor model in which the electroweak symmetry breaking is communicated to the quarks and leptons by technicolored $SU(2)_W$-singlet scalars. When the technifermions condense, the quarks and leptons of the…
In the $SO(5) \times U(1) \times SU(3)$ gauge-Higgs unification in the Randall-Sundrum warped space the mixing in the $W$ couplings in the quark sector is induced by masses of $SO(5)$ singlet fermions which are responsible for splitting…
I present an argument, based on the topology of the universe, why there are three generations of fermions. The argument implies a preferred unified gauge group of SU(5), but with SO(10) representations of the fermions. The breaking pattern…
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 family unification in grand unified theory (GUT) based on an $SU(19)$ GUT gauge group broken to its subgroups including a special subgroup. In the $SU(19)$ GUT on the six-dimensional (6D) orbifold space $M^4\times…
We present a first-principles derivation of the masses of all twelve known fermions -- three charged leptons, six quarks, and three neutrinos -- and the fine-structure constant $\alpha^{-1}$, from a single discrete functional equation, the…
Using a dimensional reduction formula for the lattice fermion determinant we study canonical determinants on quenched SU(3) gauge configurations. The canonical determinants decribe a fixed quark number and we analyze their properties below…
We use coherent states as trial states for a variational approach to study a system of a finite number of three-level atoms interacting in a dipolar approximation with a one-mode electromagnetic field. The atoms are treated as…
Conserved quantities are crucial in quantum physics. Here we discuss a general scenario of Hamiltonians. All the Hamiltonians within this scenario share a common conserved quantity form. For unitary parametrization processes, the…
The main thesis of this paper deals with the interactions of a set of fermions which are described by one basic type of bilinear interactions,two symmetric semiobjects,three embedded shells and four fundamental (strong)…
Quantum algebras U_q(su_n) used as the algebras of flavour symmetry (usually described by SU(n)) to study static properties of hadrons lead to intriguing results. In this contribution we focus on the peculiar properties manifested by…
The spherical to deformed $\gamma -unstable$ shape- phase transition in odd-A nuclei is investigated by using the Dual algebraic structures and the affine $SU(1,1)$ Lie Algebra within the framework of the interacting boson - fermion model.…