Classical Limit of the Three-Point Function from Integrability

We give analytic expression for the three-point function of three large classical non-BPS operators N=4 Super-Yang-Mills theory at weak coupling. We restrict ourselves to operators belonging to an su(2) sector of the theory. In order to carry out the calculation we derive, by unveiling a hidden factorization property, the thermodynamical limit of Slavnov's determinant.Comment: 4 pages, 2 figure

Construction of Monodromy Matrix in the F- basis and Scalar products in Spin Chains

We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin - 1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in terms of the elements of the Monodromy matrix. We use this results to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the direct correspondence between the calculations of scalar products in the F- basis and the usual basis.Comment: LaTex, 20 page

Twisted Quantum Lax Equations

We give the construction of twisted quantum Lax equations associated with quantum groups. We solve these equations using factorization properties of the corresponding quantum groups. Our construction generalizes in many respects the Adler-Kostant-Symes construction for Lie groups and the construction of M. A. Semenov Tian-Shansky for the Lie-Poisson case.Comment: 23 pages, late

Supersymmetric Vertex Models with Domain Wall Boundary Conditions

By means of the Drinfeld twists, we derive the determinant representations of the partition functions for the $gl(1|1)$ and $gl(2|1)$ supersymmetric vertex models with domain wall boundary conditions. In the homogenous limit, these determinants degenerate to simple functions.Comment: 19 pages, 4 figures, to be published in J. Math. Phy

Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model

We solve the operator ordering problem for the quantum continuous integrable su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum trace identities, and the spectrum for the higher-order local charges. We also show that this method, based on operator regularization and renormalization, which guarantees quantum integrability, as well as the construction of self-adjoint extensions, can be used as an alternative to the discretization procedure, and unlike the latter, is based only on integrable representations.Comment: 27 pages; misprints corrected, references adde