Related papers: A Possible SLq(2) Substructure of the Standard Mod…
In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston's geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement…
Superconducting quantum symmetries in extended single-band 1-dimensional Hubbard models are shown to originate from the classical (pseudo-)spin SO(4) symmetry of a class of models of which the standard Hubbard model is a special case.…
In the present paper we construct all typical finite-dimensional representations of the quantum Lie superalgebra $U_{q}[gl(2/2)]$ at generic deformation parameter $q$. As in the non-deformed case the finite-dimensional…
We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative…
The renormalizable coloron model constitutes the minimal extension of the standard model (SM) color sector to $SU(3)_{1c} \times SU(3)_{2c}$, with the spontaneous symmetry breaking of the extended gauge group to the diagonal QCD facilitated…
We suggest the model with the gauge group $ ... \otimes SU(6) \otimes SU(5)\otimes SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$. This group is the infinite continuation of the gauge group $SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$…
Knot polynomials colored with symmetric representations of $SL_q(N)$ satisfy difference equations as functions of representation parameter, which look like quantization of classical ${\cal A}$-polynomials. However, they are quite difficult…
In the context of conventional quantum field theory, we present a general Lorentz-violating extension of the minimal SU(3) x SU(2) x U(1) standard model including CPT-even and CPT-odd terms. It can be viewed as the low-energy limit of a…
Let (\Gamma,d) be the 3D-calculus or the 4D_{\pm}-calculus on the quantum group SU_q(2). We describe all pairs (\pi, F) of a *-representation \pi of O(SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical…
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…
A knot $K\subset S^3$ is called $SU(2)$-abundant if it satisfies two conditions: first, for all but finitely many $r\in\mathbb{Q}\backslash\{0\}$, there exists an irreducible representation $\pi_1(S^3_r(K))\to SU(2)$; second, any slope…
Peering in from the outside, $\mathbb{A} := \mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$ looks to be an ideal mathematical structure for particle physics. It is 32 $\mathbb{C}$-dimensional: exactly the size of one full…
Seven commuting elements of the Clifford algebra $Cl_{7,7}$ define seven binary eigenvalues that distinguish the $2^7=128$ states of 32 fermions, and determine their parity, electric charge and interactions. Three commuting elements of the…
Semiclassical quantization of the SU(3)-skyrmions is performed by means of the collective coordinate method. The quantization condition known for the SU(2)-solitons quantized with SU(3) collective coordinates is generalized for the SU(3)…
A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical…
We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. Our methods are rooted in the bracket…
A primitive completely normal element for an extension $\mathbb{F}_{q^n}/\mathbb{F}_{q}$ of Galois fields is a generator of the multiplicative group of $\mathbb{F}_{q^n}$, which simultaneously is normal over every intermediate field of that…
We present a class of N=1 supersymmetric ``standard'' models of particle physics, derived directly from heterotic M-theory, that contain three families of chiral quarks and leptons coupled to the gauge group SU(3)_C X SU(2)_L X U(1)_Y.…
We show that a quantum deformation of quantum mechanics given in a previous work is equivalent to quantum mechanics on a nonlinear lattice with step size $\Delta x=~(1-q)x$. Then, based on this, we develop the basic formalism of quantum…
We study an extension of the gauge group SU(3)_c X SU(2)_L X U(1)_Y of the standard model to the symmetry group SU(3)_c X SU(4)_L X U(1)_X (3-4-1 for short). This extension provides an interesting attempt to answer the question of family…