34870247
Vertex operators in solvable lattice models
The basic properties of q‐vertex operators are formulated in the context of the Andrews–Baxter–Forrester (ABF) series, as an example of face interaction models, the q‐difference equations satisfied by their correlation functions are derived, and their connection with representation theory established. The q‐difference equations of the Kashiwara–Miwa (KM) series are discussed as an example of edge interaction models. Next, the Ising model, the simplest special case of both ABF and KM series, is studied in more detail using the Jordan–Wigner fermions. In particular, all matrix elements of vertex operators are calculated.
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 
 
.
197508512
TRANSFORMATION GROUPS FOR SOLITON EQUATIONS. 6. KP HIERARCHIES OF ORTHOGONAL AND SYMPLECTIC TYPE
120357954
New R Matrices Associated with Cyclic Representations of Uq(A2(2))
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.
120444359
New results from GRACE/SUSY at 1-loop
We discuss the physical importance of the 1-loop correction for several supersymmetric processes. The on-shell renormalization scheme in the framework of the MSSM is adopted and 1-loop amplitudes are full-automatically calculated with GRACE system. The system GRACE/SUSY is checked by the independence on the nonlinear gauge parameters.
119094900
A System for the Automatic Computation of Cross-Sections Including SUSY Particles
We introduce a new method to treat Majorana fermions on the GRACE system, which has already been developed for the computation of the matrix elements for the processes of the standard model. In the standard model, we already have included such particles as Dirac fermions, gauge bosons and scalar bosons in the system. On the other hand, there are four Majorana fermions called neutralinos in the minimal SUSY standard model (MSSM). In consequence, we have constructed a system for the automatic computation of cross-sections for the processes of the MSSM. It is remarkable that our system is also applicable for another model including Majorana fermions once the definition of the model file is given.