7,984 research outputs found
The SU(n) invariant massive Thirring model with boundary reflection
We study the SU(n) invariant massive Thirring model with boundary reflection.
Our approach is based on the free field approach. We construct the free field
realizations of the boundary state and its dual. For an application of these
realizations, we present integral representations for the form factors of the
local operators.Comment: LaTEX2e file, 27 page
Free field approach to diagonalization of boundary transfer matrix : recent advances
We diagonalize infinitely many commuting operators . We call these
operators the boundary transfer matrix associated with the quantum
group and the elliptic quantum group. The boundary transfer matrix is related
to the solvable model with a boundary. When we diagonalize the boundary
transfer matrix, we can calculate the correlation functions for the solvable
model with a boundary. We review the free field approach to diagonalization of
the boundary transfer matrix associated with and
. We construct the free field realizations of the
eigenvectors of the boundary transfer matrix . This paper includes new
unpublished formula of the eigenvector for . It is thought that
this diagonalization method can be extended to more general quantum group
and elliptic quantum group .Comment: To appear in Group 28 : Group Theoretical Method in Physic
The Riemann-Hilbert problem associated with the quantum Nonlinear Schrodinger equation
We consider the dynamical correlation functions of the quantum Nonlinear
Schrodinger equation. In a previous paper we found that the dynamical
correlation functions can be described by the vacuum expectation value of an
operator-valued Fredholm determinant. In this paper we show that a
Riemann-Hilbert problem can be associated with this Fredholm determinant. This
Riemann-Hilbert problem formulation permits us to write down completely
integrable equations for the Fredholm determinant and to perform an asymptotic
analysis for the correlation function.Comment: 21 pages, Latex, no figure
The Integrals of Motion for the Deformed W-Algebra II: Proof of the commutation relations
We explicitly construct two classes of infinitly many commutative operators
in terms of the deformed W-algebra , and give proofs of the
commutation relations of these operators. We call one of them local integrals
of motion and the other nonlocal one, since they can be regarded as elliptic
deformation of local and nonlocal integrals of motion for the algebra.Comment: Dedicated to Professor Tetsuji Miwa on the occasion on the 60th
birthda
Difference equations for the higher rank XXZ model with a boundary
The higher rank analogue of the XXZ model with a boundary is considered on
the basis of the vertex operator approach. We derive difference equations of
the quantum Knizhnik-Zamolodchikov type for 2N-point correlations of the model.
We present infinite product formulae of two point functions with free boundary
condition by solving those difference equations with N=1.Comment: LaTEX 16 page
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