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We study the dispersions of the guided modes in the continuous uniaxial crystal slab waveguide and engineer their degeneracies through dielectric anisotropy. By switching the uniaxial positivity and negativity, we can obtain distinctive nodal types, point and line, for the lowest degeneracy in frequency. The mirror symmetry protections, Mx and My, are pointed out, and the degeneracy properties are intuitively analyzed through comparing the approximate slopes of the guided modes. Our results reveal a link between the lowest nodal types and the positivity/negativity of the uniaxial crystal, and provide a new approach to regulate the topology of degeneracy in two-dimensional photonic bands.

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.

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

Following the construction of the projection operators on $T^2$ presented by Gopakumar, Headrick and Spradlin, we construct a set of projection operators on the integral noncommutative orbifold $T^2/G (G=Z_N, N=2, 3, 4, 6)$ which correspond to a set of solitons on $T^2/Z_N$ in noncommutative field theory. In this way, we derive an explicit form of projector on $T^2/Z_6$ as an example. We also construct a complete set of projectors on $T^2/Z_N$ by series expansions for integral case.

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.

In this paper, we propose a supersymmetric SU(1|2) Gaudin model and have derived its eigenvalues. We also present the well-defined eigenstates through the quasi-classical limit of the eigenstates in the supersymmetric t-J model.

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.

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

By using the fusion method, we give the spin-1 XXX chain associated with sl2 with two arbitrary spin boundary impurities. Then the exact diagonalized Hamiltonian of this model was obtained by the means of Bethe ansatz method.

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.

We propose the eigenstates and eigenvalues of Hamiltonians of the rational SU(N) Gaudin model based on the quasi-classical limit of the SU(N) chain under the periodic boundary condition. Using the quantum inverse scattering method, we also obtain the eigenvalues of the generation function of the rational SU(N) Gaudin model.

By imposing conformally broken constraints on SL(2,R) WZNW model, we obtain a new classical completely integrable system which contains the famous sinh-Gordon system as a special case. The integrability of this extended sink-Gordon system is exhibited by the existence of the Lax pair with spectral parameters. And its funda-mental .Poisson-Lie brackets can be ultralocalized, corresponding classical r-matrix depends on two spetral parameters and satisfies the classical Yang-Baxter equation. After a suitable automorphic transformation of the loop algebra on which the above Lax pair takes value, such an ultralocalized r-matrix can be classified to the so-cal-led trigonometric type of r-matrices depending essentially on one spectral parameter.

This note shows that the nontrivial third order cohomology cycle for gauge group implies the existence of anomalous associative law and consequently anomaly for Jacobi identity.

We give maps onto a SO(3) subgroup manifold of the SU(3) group manifold, which is reducible to a CP(1) and a CP(2) chiral field. The map on CP(1) is holomorphic, while that on CP(2) may be either holomorphic or not. We also discuss the related gauge field and cohomology properties.

We discuss the XXZ spin chain with certain boundary term and the representation of quantum group SUq(2). It is shown that Bethe Ansatz states are highest weight states of SUq(2), with q arbitrary We construct the irreducible representation of the quantum group. For q a rational root of unity, we show that there are new solutions to the BA equations, We derived the state vectors | b′> by taking certain limit, from which we construct the type I and type Ⅱ representations of SUq(2).

The Hamiltonian of a 1D quantum chain corresponding to Belavin's zn × zn symmetric model is derived. This Hamiltonian is a multicomponent generalisation of the XYZ model with n2 coupling constants in general. In the limit tau to i infinity it reduces to the generalised XXZ model with (n-1) n-fold-degenerate coupling constants and n non-degenerate ones. The Hamiltonian is Hermitian only for n=2 or for n > 2 with a crossing parameter w restricted to integers. There exists a domain of parameters in which the Boltzmann weights are positive but the corresponding Hamiltonian is non-Hermitian. The relations of the Hamiltonian to other models are discussed.

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.

The quantum and classical algebras connected with the Zn‐symmetric elliptic solution of the Yang–Baxter equation are derived; their structure constants and the relations between the quantum algebra and the classical one are investigated in detail. Moreover, the trigonometric limit of these algebras is worked out.

The algebraic regularity of monopole eigenfunctions in various dynamical O (2,1) bases shows the symmetry in radial phase space. The multipole tensors serve as ladder operators between different O (2,1)⊗ O (3) quasi-bound states.

In this paper, we show that the SO(3) chiral field can be regard as the normal Vector field over the pseudo-spherical surface, and thus obtain the correspondence between chiral field and sine-Gordon system, as well as the geometrical interpretation of chiral field. By means of the dual symmetry between chiral field and the pseudo-spherical surface, we are able to connect chiral field with s-G system, and express Backlund transformation, Riccati equation in the gauge invariant representations of the related properties of the same dynamical system in different frames.

This paper studies explicitly the Abelian spontaneously broken gauge model for scalar and gauge bosons by using perturbation expansions . It is discovered that in various renormalizable gauges (R gauge) the gauge dependent part contributed by unphysical components of inner lines in the sum of all Feynman diagrams of the same order coexists only with the outer mass shell components of outer lines. On the mass shell only the contribution by physical components is left, just as in the unitary gauge (U gauge). Thus, the identitical nature of the R gauge and U gauge on the mass shell has been shown explicitly, hence may be seen the unitarity of the R gauge. It is also shown why residue divergences appear in the U gauge, and why these residue divergences will necessarily cancal each other out, thus revealing the crypto-renormali-zability of the U gauge.

In this paper, we present a new transformation in the solution space of the Ernst equation and investigat the relationship between the solutions of the Ernst equation and our transformation. We show that the Ernst equation is invariant under such a transformation, i.e., our transformation can be used to generate the new solutions of the Ernst equation from the old ones. Finally, we discuss the relationship between the Virasoro algebra and this transformation.