2947742
Difference equations in spin chains with a boundary
Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite spin chain systems with integrable boundary conditions. We derive these equations using the properties of the vertex operators and the boundary vacuum state, or alternatively through corner transfer matrix arguments for the eight-vertex model with a boundary. The spontaneous boundary magnetization is found by solving such difference equations. The boundary S-matrix is also proposed and compared, in the sine-Gordon limit, with Ghoshal-Zamolodchikov's result. The axioms satisfied by the form factors in the boundary theory are formulated.
11481265
Reduced qKZ Equation and Correlation Functions of the XXZ Model
Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations. The main relations among them are the difference equations obtained from the qKZ equation by specializing the variables (λ1, . . . ,λ2n) as (λ1, . . . ,λn,λn+1, . . . ,λ1+1). We call it the reduced qKZ equation. In this article we construct a special family of solutions to this system. They can be written as linear combinations of products of two transcendental functions ,ω with coefficients being rational functions. We show that correlation functions of the XXZ model in the massive regime are given by these formulas with an appropriate choice of ,ω. We also present a conjectural formula in the massless regime.
73711304
Solitons and Infinite-Dimensional Lie Algebras
Introduction §1. Fock Representation of gf(°°) §2. T Functions and the KP Hierarchy §3. Reduction to A[" §4. Fermions with 2 Components §5. Algebras B^ and Co §6. Spin Representation of J&TO §7. Algebras D^ and £C §8. Reduction to Kac-Moody Lie Algebras §9. Time Evolutions with Singularities Other than k = 00 —The 2 Dimensional Toda Lattice— §10. Difference Equations —The Principal Chiral Field— Appendix 1. Bilinear Equations for the (Modified) KP Hierarchies Appendix 2. Bilinear Equations for the 2 Component Reduced KP Hierarchy Appendix 3. Bilinear Equations Related to the Spin Representations of Bca Appendix 4. Bilinear Equations Related to the Spin Representations of D^
120357954
New R Matrices Associated with Cyclic Representations of Uq(A2(2))
117124186
Branching rules for quantum toroidal gl(n)
We construct an analog of the subalgebra $Ugl(n)\otimes Ugl(m)$ of $Ugl(m+n)$ in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.
117707944
Quantum R matrix related to the generalized Toda system: An algebraic approach
We report on some recent progress concerning the Yang-Baxter equation and related algebraic structures -the q-analogue 
 
of the universal enveloping algebra and the Hecke algebra. The results include 1) construction of trigonometric R matrices related to the vector representation of non-exceptional Lie algebras, ii) construction of representations of 
 
for 
 
, and iii) existence of R for a class of representations of 
 
.
118485809
Slepton NLG (Non-Linear Gauge) in GRACE/SUSY-loop
We have been developing a program package calledGRACE/SUSY-loop which is for the automatic calculations of the MSSM amplitudes in one-loop order. The non-linear gauge (NLG) fixing conditions play the crucial role in the calculations in one-loop order which contain a large number of Feynman diagrams. We present the recent progress inGRACE/SUSY-loop which is obtained by extending the non-linear gauge formalism to the slepton sector.
117876117
Present Status of GRACE/SUSY-loop
GRACE/SUSY-loop is a program package for the automatic calculation of the MSSM amplitudes in one-loop order. We present features of GRACE/SUSY-loop, processes calculated using GRACE/SUSY-loop and an extension of the non-linear gauge formalism applied to GRACE/SUSY-loop.