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^
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.
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.
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.
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.
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-
16969156
The SUSY-GRACE system
We introduce a new method to treat Majorana fermions on the GRACE system which has been developed for the computation of the matrix elements for the processes of the standard model. In the standard model, we already have such particles as Dirac fermions, gauge bosons and scalar bosons in the system. 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. It is remarkable that our system is also applicable to
15619161
Automatic Calculation of SUSY-particle Production )
AbstractWe introduce a new method to treat Majorana fermions and interactions with fermion-number violation on the GRACE system which has been developed for the automatic com-putation of the matrix elements for the processes of the standard model. Thus we haveconstructed a system for the automatic computation of cross-sections for the processes of theminimal SUSY standard model (MSSM). 1 Introduction At the theoretical point of view, it has been a promising hypothesis that there exists a symmetry calledsupersymmetry (SUSY) between bosons and fermions at the uniﬁcation-energy scale. It, however, is abroken symmetry at the electroweak-energy scale. Thus the relic of SUSY is expected to remain as a richspectrum of SUSY particles, partners of usual matter fermions, gauge bosons and Higgs scalars, namedsfermions, gauginos and higgsinos, respectively [1].The quest of these new particles has already been one of the most important pursuits to the presenthigh-energyphysics[2]. Although suchparticleshavenot yet been discovered, massesofthem areexpectedto be O(10
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.
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.
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.