Related papers: A Possible SLq(2) Substructure of the Standard Mod…
We apply a recently proposed mechanism -- in which an SU(3) symmetry predicts the weak mixing angle -- to construct realistic theories with composite quarks and leptons at a TeV. Although the models are strongly coupled, they are reliably…
The quantum flag manifold ${SU_q(3)/\mathbb{T}^2}$ is interpreted as a noncommutative bundle over the quantum complex projective plane with the quantum or Podle\'s sphere as a fibre. A connection arising from the (associated) quantum…
The Jones-Witten theory gives rise to representations of the (extended) mapping class group of any closed surface Y indexed by a semi-simple Lie group G and a level k. In the case G=SU(2) these representations (denoted V_A(Y)) have a…
We express the discrete 1+1-dimensional $O(3)$ non-linear sigma model (NL$\sigma$M) in a form well-suited for the continuous variable approach to quantum computing. Within the Schwinger boson formulation, we need two qumodes…
This article investigates the construction of fermions and the formulation of the Standard Model of particle physics in a theory in which the Lorentz signature emerges from an underlying microscopic purely Euclidean $SO(4)$ theory.…
In this paper, we explore natural connections among the representations of the extended affine Lie algebra $\widehat{sl_N}(\mathbb{C}_q)$ with $\mathbb{C}_q=\mathbb{C}_q[t_0^{\pm1},t_1^{\pm1}]$ an irrational quantum 2-torus, the simple…
In a scheme originally proposed by M. Gell-Mann, and subsequently shown to be realized at the SU(3)xU(1) stationary point of maximal gauged SO(8) supergravity by N. Warner and one of the present authors, the 48 spin 1/2 fermions of the…
We construct two SU(5) models on the space-time $M^4 \times T^2/(Z_2 \times Z_2^{\prime})$ where the gauge and Higgs fields are in the bulk and the Standard Model fermions are on the brane at the fixed point or line. For the zero modes, the…
The quantum group analogue of the normalizer of SU(1,1) in SL(2,C) is an important and non-trivial example of a non-compact quantum group. The general theory of locally compact quantum groups in the operator algebra setting implies the…
The spectrum of $\Lambda$ and $\Sigma$ excitations is reviewed taking into account (nearly) all hyperon resonances which were seen in early analyses or in one of the recent partial-wave analyses. The spectrum is compared with the old…
We present a model for the vector and axial form factors of the transitions $\overline{B}^0 \to D^{**}$ in good agreement with the presently available data and based on the present theoretical knowledge, combining a) the safe lattice QCD…
The Peccei-Quinn ($PQ$) mechanism is applied to the $\mathrm{SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model with $U(1)_{B-L}$ symmetry. The structures in the $PQ$ charges of all fermions and scalar fields in the model are investigated by…
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
A phenomenological analysis of the three-family model based on the local gauge group $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ with exotic charged leptons, is carried out. Instead of using the minimal scalar sector able to break the symmetry…
Two-dimensional spin-orbital magnets with strong exchange frustration have recently been predicted to facilitate the realization of a quantum critical point in the Gross-Neveu-SO(3) universality class. In contrast to previously known…
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…
Pairing between the universal enveloping algebra $U_q(sl(2))$ and the algebra of functions over $SL_q(2)$ is obtained in explicit terms. The regular representation of the quantum double is constructed and investigated. The structure of the…
A fermion-boson-type Composite Model is proposed. Elementary fields are only one kind of spin-1/2 and spin-0 {\bf preon}. Both are in the global supersymmetric pair with the common electric charge of e/6 and belong to the fundamental…
We study predictions of orbifold family unification models with $SU(9)$ gauge group on a six-dimensional space-time including the orbifold $T^2/Z_2$, and obtain relations among sfermion masses in the supersymmetric extension of models. The…
Irreducible representations of quantum groups $SL_q(2)$ (in Woronowicz' approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the~case of $q$ being an~odd root of unity. Here we find the~irreducible representations for all…