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

Correlators of the phase model

We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the "darkness formation probability" are calculated in the thermodynamical limit. These results can be used to construct integrable equations for the correlation functions and to calculate there asymptotics.Comment: LaTeX, 7 pages, One reference has been change

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

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

Comultiplication in ABCD algebra and scalar products of Bethe wave functions

The representation of scalar products of Bethe wave functions in terms of the Dual Fields, proven by A.G.Izergin and V.E.Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in \cite{Izergin87} and \cite{Korepin87} is based on the explicit expression for the "senior" coefficient which was guessed in \cite{Izergin87} and then proven to satisfy some recurrent relations, which determine it unambiguously. In this paper we present an alternative proof based on the direct computation.Comment: 9 page