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

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

Temperature Correlation of Quantum Spins

This is a historical note. In 1993 we calculated space, time and temperature dependent correlation function in isotropic version of one dimensional XY spin chain. The correlation function decays exponentially with time and space separation. The rate of exponential decay was evaluated explicitly. Since that time similar results were obtained in other models: Bose gas with delta interaction, Ising model and strongly correlated electrons.Comment: 8 page