Related papers: A Note on the Two-Level Pairing Model Obeying the …
We exploit the SU(N) irreducible Schwinger boson to construct SU(N) coherent states. This construction of SU(N) coherent state is analogous to the construction of the simplest Heisenberg-Weyl coherent states. The coherent states belonging…
We consider the conditions under which the $q$-oscillator algebra becomes a Hopf $*$-algebra. In particular, we show that there are at least two real forms associated with the algebra. Furthermore, through the representations, it is shown…
The significant heavy threshold effect is found in the supersymmetric SU(5) model with two adjoint scalars, one of which is interpreted as a massive string mode decoupled from the lower-energy particle spectra. This threshold related with…
We investigate the twelve-dimensional gauge-Higgs unification models with an eight-dimensional coset space. For each model, we apply the coset space dimensional reduction procedure and examine the particle contents of the resulting…
Using a complex deformation q=exp(is) of su(2) we obtain extensions of the finite-dimensional representations towards the infinite-dimensional ones. A generalised q-deformation of su(2), as a Hopf algebra is introduced. We present the…
In this work, we refine recent results on the explicit construction of polynomial algebras associated with commutants of subalgebras in enveloping algebras of Lie algebras by considering an additional grading with respect to the subalgebra.…
We develop the dual description of $2+1$ SU(2) lattice gauge theory as interacting `abelian like' electric loops by using Schwinger bosons. "Point splitting" of the lattice enables us to construct explicit Hilbert space for the gauge…
One-dimensional lattice model of SU(2)_{4} anyons containing a transition into the topological ordered phase state is considered. An effective low-energy Hamiltonian is found for half-integer and integer indices of the type of strongly…
As I briefly review, the sine-Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self-dual U(2) Yang-Mills through a 2+1 dimensional integrable U(2) sigma model. I argue that the noncommutative (Moyal)…
We study a possibility of the Higgs boson, which consists of an SU(2) doublet and a septet. The vacuum expectation value of a septet with hypercharge Y=2 is known to preserve the electroweak rho parameter unity at the tree level. Therefore,…
Considering anyonic oscillators in a two-dimensional lattice, we realize the quantum semi-group $sl_{(q,s)}(2)$ by means of a generalized Schwinger construction. We find that the parameter $q$ of the algebra is connected to the statistical…
We propose the two-leg fermion-ladder models for SU(2|2) and SU(4) cases. The former is exactly the extended Hubbard model proposed by Essler, Korepin and Schoutens. The later is a new model also with $\eta$-pairing symmetry which is…
The dualised formulation of the symmetric space sigma model is peformed for a general scalar coset G/K where G is a maximally non-compact group and K is it's maximal compact subgroup.By using the twisted self-duality condition the general…
For a Hamiltonian system in R^{2n}, its two-system is defined in the phase space R^{2n} x sp(2n,R). In a sense, it is a combination of the original system and its system in variations with feedback. We study the Hamiltonian forms of the…
The algebra su(2) is derived from two commuting quon algebras for which the parameter q is a root of unity. This leads to a polar decomposition of the shift operators of the group SU(2). The Wigner-Racah algebra of SU(2) is developed in a…
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for D between 3 and 7. The level decomposition with respect to the U-duality Lie algebra gives…
We review the algebraic approach to super non-Abelian T-Duality considered in [1], focusing on symmetric and semi-symmetric coset spaces on $G/H$. We discuss a potential impediment, appearing in these models when integrating out the gauge…
In this paper, we generalize Schur-Weyl duality and Morita Theorem on associative algebras to those on associative $H$-pseudoalgebras. Meanwhile, we get a plenty of associative $H$-pseudoalgebras over a cocommutative Hopf algebra $H$.
In this manuscript we study the Double SU(4) model as a grand unified theory based on the gauge group $\,SU(4)\times SU(4)\left(\times \mathcal{Z}_2\right)$. A complete set of generators is constructed according to a pattern of symmetry…
Standard SUSY-GUTs such as those based on $SU(5)$ or $SO(10)$ lead to predictions for the values of $\alpha _s$ and $sin^2\theta _W$ in amazing agreement with experiment. In this article we investigate how these models may be obtained from…