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In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator on the rational noncommutative orbifold T2/Z4. we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.

The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.

From the ? symmetric action of IIB string in AdS2?S2 background given by Zhou, we derive the equations of motion. By using the twisted dual transformation which was introduced by Hou, we construct the flat currents, conserving non-local charge with one free parameter, for the superstring in AdS2?S2.

We study the quantum standard teleportation based on the generic measurement bases. It is shown that the quantum standard teleportation does not depend on the explicit expression of the measurement bases. We have given the correspondence relation between the measurement performed by Alice and the unitary transformation performed by Bob. We also prove that the single particle unknown states and the two-particle unknown cat-like states can be exactly transmitted by means of the generic measurement bases and the correspondence unitary transformations.

In this paper, we recast the matter part of the open superstring star in the present of a constant B field. By using a different coordinate representation the matter part of the open superstring star is identified with the continuous Moyal product of functions of anti-commuting variables. Fortunately we find it does not depend on the value of the B field.

In this paper we generalize the standard teleportation to the conclusive teleportation case which can teleport an arbitrary d-dimensional N-particle unknown state via the partially entangled quantum channel. We show that only if the quantum channel satisfies a constraint condition can the most general d-dimensional N-particle unknown state be perfect conclusively teleported. We also present a method for optimal conclusively teleportation of the N-particle states and for constructing the joint POVM which can discern the quantum states on the sender's (Alice's) side. Two typical examples are given so that one can see how our method works.

The effective action of chiral QCD2 was studied in two-dimensional non-commutative space-time by using path integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains a term corresponding to a Wess–Zumino–Witten-like term.

By constructing close one cochain density ${\Omega^1}_{2n}$ in the gauge group space we get WZW effective Lagrangian on high dimensional non-commutative space.Especially consistent anomalies derived from this WZW effective action in non-commutative four-dimensional space coincides with those by L.Bonora etc., Comment: 9 pages, latex, no figures

We propose a rational quantum deformed nonlocal currents in the homogenous space $SU(2)_k/U(1)$, and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level $k=c$ is obtained. In the classical limit $\hbar \to 0$, the quantum nonlocal currents become $SU(2)_k$ parafermion, and the realization of Yangian double becomes the parafermion realization of $SU(2)_k$ current algebra., Latex, 9 pages

The Hamiltonians of the SU(3) Gaudin model are constructed based on the nonrelativistic limit of the SU(3) chain. After the quantum determinant being well defined, the eigenvectors and eigenvalues of the Hamiltonians of the SU(3) Gaudin model are given. These results can be generalized to any number of constituting spins (SU(N)).

We derive a free boson representation of the Yangian double DY(slN) with arbitrary level k by the observation that there is a correspondence between the q-affine algebra and Yangian double associated with the same Cartan matrix. Vertex operator and screening currents cannot be obtained in the same way. From this point of view, the Yangian double with centre cannot be regarded as the degenerated case of the quantum affine algebra.

The Lax pair and corresponding boundary K-matrices for the XXC model are derived. The time-independent transfer matrix with the spectral parameter is constructed, which means the system to be Lax integrable. Our K-matrices include the result used by Arnaudon and Maassarani (D. Arnaudon and Z. Maassarani, lapth-695/98, laval-phy-22/98) as a special case.

We propose a dynamical elliptic algebra which is based on the relations RLL = LLR*, where R and R* are the dynamical R-matrices of -type face model with the elliptic module shifted by the center of algebra. nom the high-rank Gauss decomposition,h we obtain the Drinfeld currents of dynarnical elliptic algebra .

By using algebraic Bethe ansatz method, we give the Hamitonian of the spin-1 XXX chain associated with $sl_2$ with two boundary impurities., 8 pages, latex, no figures, to be appeared in Commun. Theor. Phys

As the Yangian double with center, which is deformed from affine algebra by the additive loop parameter ħ, we get the commutation relation and the bosonization of quantum ħ-deformed Virasoro algebra. The corresponding Miura transformation, the associated screening operators and the BRST charge have been studied. Moreover, we also construct the bosonization for type I and type II intertwiner vertex operators. Finally, we show that the commutation relations of these vertex operators in the case of and actually give the exact scattering matrix of the restricted sine-Gordon model.

After introducing briefly the basic concept of statistical interaction, we illustrate it on integrable XXZ chain corresponding Potts case by the Bethe ansatz and point out that the nontrivial part of this statistical interaction comes from the rates of change of phase shifts with respect to momentum.

Boundary operators and boundary ground states in sine-Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators. We also study the boundary bound state for this case.

A free field representation for the left-right asymmetric conformal Toda theory based on simply-laced even-rank Lie algebras is given. It is shown that the classical chiral exchange algebra for such theories can be reconstructed from free chiral bosons via Drinfeld-Sokolov linear systems, and is a bit more complicated than that of the standard Toda due to some additional -function terms and extra degrees of freedom.

By compactifying the four-dimensional Euclidean space into S2 × S2 manifold and introducing two topological relevant Wess–Zumino terms to Hn ≡ SL(n,c)/SU(n) nonlinear sigma model, we construct a Lagrangian form for SU(n) self-dual Yang–Mills field, from which the self-dual equations follow as the Euler–Lagrange equations.

This paper deals with a class of q-deformations of Heisenberg algebra which contains the q-Heisenberg algebra, the q-oscillator algebra and others. Their representation theory is considered for q being generic or a root of 1. Finally, the structure of Hopf algebra in a quotient algebra is also discussed.

In this paper, we showed that the eigenvalues of two-dimensional angular momentum of a particle with charge e are integer valued. The problems of a Dirac particle in a field of vortex were discussed. When the vortex tends-to string, we found that the system admits of the existence of θ vacua. For massless fermions, a change in θ is equivalent to a Γs rotation, while the physical result is independent of θ. For massive fermions, CP invariance is broken except for θ=0, π; and the system exhibits the Witten effect.

In this paper we show the scattering problem's equation of principal chiral model with Wess-Zumino-Witten term. Two sets of symmetry transforms are given and four series of conserved currents are obtained, in which two of them are Noether types and the others are not. Finally the Kac-Moody algebra is discussed.

In this paper, a 3-cocycle is realized in a hybrid chiral bag model as quantities at the boundary of the bag. The equivalence between charges of gauged boson currents in Skyrme model and full gauge transformation generators is established both in dimensions and dimensions.

Following the work of Wilczek and Zee, we analysed the various representatives of the elements in CP (1) chiral model and obtained the gauge potential Aμ naturally and geometrically. Furthermore, by using the Hopf bundle and its decomposition, the meaning and the origin of the Hopf integral can be obtained obviously and geometrically. Finally, some concrete results of the integral are also calculated.

We present a concept of cohomology of the gauge transformations, establish the homomorphic relation between this cohomology group and the Chern-Simons type characteristic class sequence, and analyse their applications to the non-Abelian anomaly, the gauge invariant Wess-Zumino effective action and the Schwinger term etc. We show that the present approach includes faddeev's song's and zumino's approaches.

In this paper we first present the gauge invariant conserved Noether current for the Yang-Mills theory, which is nonlocal is some sense. Then we introduce for the two dimensional chiral model, plain and supersymmetric, the nonlocal one-complex parameter-dependent symmetric generators, which shift the Lagrangian density by a total divergence. Both the equations of motion and the energy momentum density are invariant. The associated Noether current may be expanded analytically series of nonlocal currents.