119144130
Creation operators for the Fateev-Zamolodchikov spin chain
In previous works, we studied the problem of constructing a basis in the space of local operators for an anisotropic XXZ spin chain with spin 1/2 such that the vacuum expectation values have a simple form. For this, we introduced fermionic creation operators. Here, we extend this construction to the spin-1 case. Using a certain version of the fusion procedure, we find two doublets of fermionic creation operators and one triplet of bosonic creation operators. We prove that the basis obtained by the action of these operators satisfies the dual reduced quantum Knizhnik-Zamolodchikov equation.
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.
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.
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.
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.
122854367
Polarization Effects for Selectron Production in e+e- Collisions
125484343
Achievements beyond the standard model