131772242
Holonomic Quantum Fields
The present chapter V of our series is an application of the theory of rotation ([!]) to the lattice models. Included here are the two-dimensional Ising model ([5], [6]), a bosonic counterpart of it, the one-dimensional XY model ([12]) and the free fermion model ([14] [15] [16]). In each case we shall compute exactly the norm representation of spin operators, and hence their n-point correlation functions. The materials in this article are "time-ordered" according to the development, but we could have unified the treatment by using the path integral formalism exposed in Section 5.4 (symplectic case) and in Section 5.7 (orthogonal case). Since the first announcement of our result on the Ising model ([2] [4]), there have appeared several independent papers [9] [10] [11] that deal with the exact computation of n-point functions. We emphasize that these results are made most transparent by considering directly the explicit form of spin operators. (For instance the arbitrariness in the infinite series expression of n-point functions for T>TC is neatly described in this way. See p. 548.) The plan of this paper is as follows. The first three sections 5.1-5.3 are devoted to the Ising model. We shall see that a systematic application of the original method of Onsager ([5]) enables one to express explicitly not only the free energy but also the spin operator itself. We first review the diagonalization procedure of the Hamiltonian (see [5] [7]) in Section 5.1, and compute the norm representation of spin operators in Section 5.2. Using these results we derive in Section 5.3 infinite series expressions for n-point correlation functions (an application of the product formula in [1]). We also verify their convergence and several symmetry properties. In Section 5.4 we present a two-
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.
120357954
New R Matrices Associated with Cyclic Representations of Uq(A2(2))
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 
 
.
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.
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.
5722422
The automatic computation for SUSY processes
AbstractWe have constructed a system for the automatic computation of cross-sectionsfor the processesof the SUSY QED by the extension of the GRACE system includinga Majorana fermion. The system has also been applied to another model includingMajorana fermions, MSSM, by the deﬁnition of the model ﬁle. IntroductionIthas been widely believed that there exists a symmetry called supersymmetry (SUSY)between bosons and fermions at the uniﬁcation-energy scale. It, however, is a brokensymmetry at the electroweak-energy scale. The relic of SUSY is expected to remain asa rich spectrum of SUSY particles, partners of usual matter fermions, gauge bosons andHiggs scalars, named sfermions, gauginos and higgsinos, respectively [1, 2, 3].The neutral gauginos and higgsinos are Majorana fermions, which become the mixedstates called neutralinos. Since anti-particles of Majorana fermions are themselves, thereexists so-called ‘Majorana-ﬂip’, the transition between particle and anti-particle. This hasbeen the most important problem which we should solve when we realize the automaticsystem for computation of the SUSY processes.1
14459954
The GRACE system for SUSY processes
We introduce a new method to treat Majorana fermions on the GRACE system which has been developed for the automatic computation of the matrix elements for the processes of the standard model. In the GRACE system, we already have such particles as Dirac fermions, gauge bosons and scalar bosons within the standard model. On the other hand, in the SUSY models there are Majorana fermions. In the first instance, we have constructed a system for the automatic computation of cross-sections for the processes of the SUSY QED. The system has also been applied to another model including Majorana fermions, the minimal SUSY standard model (MSSM), by the re-definition of the model file.
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.
122854367
Polarization Effects for Selectron Production in e+e- Collisions
117722201
POLARIZED CROSS-SECTIONS FOR e+ e- ---> W- lepton-sneutrino slepton+
We investigate the single W production associated with sleptons in longitudinally polarized e+e- beams. The polarized cross-sections and the angular distributions of W- are calculated for charged sleptons in left-handed and right-handed multiplets. It is shown that this process will be major background one for the standard one in the single W production at √s = 1 TeV.