Related papers: A Note on the Two-Level Pairing Model Obeying the …
We construct the representations of general dimension for the soliton solution to the $SU(2)$ Skyrme model, and show that at the classical level the dependence on the dimension of the representation ($2j+1$) appears only as an overall…
We find a dual version of a previous double-bosonisation theorem whereby each finite-dimensional braided-Hopf algebra $B$ in the category of comodules of a coquasitriangular Hopf algebra $A$ has an associated coquasitriangular Hopf algebra…
Let R: V x V -> V x V be a Hecke type solution of the quantum Yang-Baxter equation (a Hecke symmetry). Then, the Hilbert-Poincre' series of the associated R-exterior algebra of the space V is a ratio of two polynomials of degree m…
Four apparently different bosonizations of the $U_q(su(2)_k)$ quantum current algebra for arbitrary level $k$ have recently been proposed in the literature. However, the relations among them have so far remained unclear except in one case.…
All Lie bialgebra structures for the (1+1)-dimensional centrally extended Schrodinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family…
We resolve the SU(3) outer multiplicity problem by defining all possible $SU(3)\otimes SU(3)$ invariant operators in terms of SU(3) Schwinger bosons. We show that the elementary invariant operators relevant to the outer multiplicity problem…
The electroweak model is formulated on the nonlinearly realized gauge group SU(2) X U(1). This implies that in perturbation theory no Higgs field is present. The paper provides the effective action at the tree level, the Slavnov Taylor…
A $\gamma$-deformed version of $su(2)$ algebra with non-hermitian generators has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. The related Jordan-Schwinger(J-S) map is combined with boson algebras to obtain a hierarchy…
An algebraic restriction of the nonabelian self-dual Chern-Simons-Higgs systems leads to coupled abelian models with interesting mass spectra. The vacua are characterized by embeddings of $SU(2)$ into the gauge algebra, and in the broken…
In this second part about dynamics of atomic system we revisit the logic application of $SU(2)$ dynamics. We reiterate that solution of quantum dynamics systems can be represented geometrically. Such geometric representations of solutions…
There exist two different languages, the ^sl(2) and N=2 ones, to describe similar structures; a dictionary is given translating the key representation-theoretic terms related to the two algebras. The main tool to describe the structure of…
We show that the equality of 2d $\mathcal{N}$=(2,2) supersymmetric indices in Seiberg-type duality leads to a new integrable Ising-type model. The emergence of the new model is the result of correspondence between the supersymmetric $SU(2)$…
In this paper we introduce the bosonic generators of the $sp(4,R)$ algebra and study some of their properties, based on the $SU(1,1)$ and $SU(2)$ group theory. With the developed theory of the $Sp(4,R)$ group, we solve the interaction part…
The (1+1)-dimensional bosonization relations for fermionic mass terms are derived by choosing a specific gauge in an enlarged gauge-invariant theory containing both fermionic and bosonic fields. The fermionic part of the generating…
Integrable $su(2\vert2)_{c}$ symmetric models have integrable boundaries with $osp(2\vert2)$ symmetries, which can be embedded into $su(2\vert2)_{c}$ in two different ways. We dualize the previously obtained asymptotic overlap formulas for…
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which…
We review the classical boson-fermion correspondence in the context of the $\widehat{sl(2)}$ current algebra at level 2. This particular algebra is ideal to exhibit this correspondence because it can be realized either in terms of three…
Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein's equations may be written in terms of an SO(3) connection, with SO(3) chosen as an appropriate…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
This article deals with a nonrelativistic quantum mechanical study of a charge-dyon system with the SU(2)--monopole in five dimensions. The Schr\"odinger equation for this system is separable in the hyperspherical and parabolic coordinates.…