119951423
TRANSFORMATION GROUPS FOR SOLITON EQUATIONS
A new approach to soliton equations, based on τ functions (or Hirota's dependent variables), vertex operators and the Clifford algebra of free fermions, is applied to study a new hierarchy of Kadomtsev-Petviashvili type equations (the BKP hierarchy). The infinite-dimensional orthogonal group acts on the space of BKP τ-functions. The Sawada-Kotera equation is obtained as a reduction of BKP. Its infinitesimal transformations constitute the Euclidean Lie Algebra A2(2).
119324041
Asymptotic representations and Drinfeld rational fractions
We introduce and study a category of representations of the Borel algebra, associated with a quantum loop algebra of non-twisted type. We construct fundamental representations for this category as a limit of the Kirillov-Reshetikhin modules over the quantum loop algebra and we establish explicit formulas for their characters. We prove that general simple modules in this category are classified by n-tuples of rational functions in one variable, which are regular and non-zero at the origin but may have a zero or a pole at infinity.
14644136
Smirnov's integrals and the quantum Knizhnik-Zamolodchikov equation of level 0
We study the quantum Knizhnik-Zamolodchikov equation (1984) of level 0 associated with the spin 1/2 representation of Uq(SL2). We find an integral formula for solutions in the case of an arbitrary total spin and mod q mod <1. In the formula, different solutions can be obtained by taking different integral kernels with the cycle of integration being fixed.
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-
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.
125484343
Achievements beyond the standard model
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.
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.
120133529
Two-body and three-body decays of charginos in one-loop order in the MSSM
We present the renormalization scheme used in and the characteristic features of GRACE/SUSY-loop, the package of the program for the automatic calculation of the minimal supersymmetric standard model processes including one-loop order corrections. The two-body and three-body decay widths of charginos in one-loop order evaluated by GRACE/SUSY-loop are shown.
121759891
The GRACE system for the minimal supersymmetric standard model
The algorithm of constructing the Feynman amplitudes for the GRACE system is extended to processes involving supersymmetric particles. New vertex amplitude subroutines needed to compute these processes are now part of the CHANEL library.