333 research outputs found
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
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