Related papers: Trefoil Solitons, Elementary Fermions, and SU_q(2)
We attempt to go beyond the standard electroweak theory by replacing SU(2) with its q-deformation: SU_q(2). This step introduces new degrees of freedom that we interpret as indicative of non-locality and as a possible basis for a solitonic…
The conjecture that the elementary fermions are knotted flux tubes permit the construction of a phenomenology that is not accessible from the standard electroweak theory. In order to carry these ideas further we have attempted to formulate…
It is shown that the four trefoil solitons that are described by the irreducible representations D^{3/2}_{mm'} of the quantum algebra SL_q(2) (and that may be identified with the four families of elementary fermions…
SU(3) gauge theory coupled to N_f = 2 fermions in the sextet representation is a promising candidate for a technicolor inspired Standard Model extension. In this note the progress in the past few years aimed at understanding the…
We examine a quantum group extension of the standard model with the symmetry $SU(3) \times SU(2) \times U(1)\times $ global $SLq(2)$. The quantum fields of this extended model lie in the state space of the $SLq(2)$ algebra. The normal modes…
We show that most of the applications of SU_q(2) fermions to statistical mechanics and quantum field theory, previously discussed in literature, are based on a wrong statement about the connection between deformed and undeformed fermion…
The q-electroweak theory suggests a description of elementary particles as solitons labelled by the irreducible representations of SU_q(2). Since knots may also be labelled by the irreducible representations of SU_q(2), we study a model of…
In this paper a loophole in the SU(2) gauge anomaly is presented. It is shown that using several topological tools a theory can be designed that implements the quantization of a single Weyl doublet anomaly free while keeping the non-abelian…
By considering a set of $N$ anyonic oscillators ( non-local, intrinsic two-dimensional objects interpolating between fermionic and bosonic oscillators) on a two-dimensional lattice, we realize the $SU_q(N)$ quantum algebra by means of a…
The idea that the elementary particles might have the symmetry of knots has had a long history. In any current formulation of this idea, however, the knot must be quantized. The present review is a summary of a small set of papers that…
In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear O(3) sigma model from the SU(2) massive gauge…
The knot model is extended by assuming that the trefoils are realized as either chiral fermions or as scalar bosons. There are then four scalar trefoils with electric charges (0, -1,2/3,-1/3) that may be classified in the same way as the…
We consider a superrenomalizable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU(2). The generating functional of the correlation functions of the gauge fields is derived and its…
Gauge theories with fermions in adjoint and fundamental representations are relevant for many different applications including composite Higgs models and general aspects of the confinement problem. We present first results from simulations…
We consider the extended electroweak gauge group SU(2)_1 \times SU(2)_2 \times U(1)_Y where the first and second families of fermions couple to SU(2)_1 while the third family couples to SU(2)_2. Bounds based an precision electroweak…
We prove that, for the quon algebra, which interpolates between the Bose and Fermi statistics and depends on a free parameter q,it is possible to build an su(2) irreducible representation. One of the consequences of this fact is that the…
Knots in the Chern-Simons field theory with Lie super gauge group $SU\left(M|N\right) $ are studied, and the $% S_{L}\left(\alpha,\beta,z\right) $ polynomial invariant with skein relations are obtained under the fundamental representation…
Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed…
The inconsistence of Dirac-Weyl field equations with the universal U(1) gauge invariance of neutrinos in quantum mechanics led to generalize the special relativity to the generic relativity, which was composed of the special relativity and…
Gauge theory on the q-deformed two-dimensional Euclidean plane R^2_q is studied using two different approaches. We first formulate the theory using the natural algebraic structures on R^2_q, such as a covariant differential calculus, a…