Annihilation Poles for Form Factors in XXZ Model

The annihilation poles for the form factors in XXZ model are studied using vertex operators introduced in \cite{DFJMN}. An annihilation pole is the property of form factors according to which the residue of the $2n$-particle form factor in such a pole can be expressed through linear combination of the $2n-2$-particle form factors. To prove this property we use the bosonization of the vertex operators in XXZ model which was invented in \cite{JMMN}.Comment: 15 pages, LATeX, RIMS-93

On the Continuum Limit of the Conformal Matrix Models

The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the paper \cite{FKN91a} is proposed, the corresponding partition functions being compared. All calculations are demonstrated in full in the first non-trivial case of $W^{(3)}$-constraints.Comment: FIAN/TD-5/92, LaTeX, 32p

Quantum relativistic Toda chain at root of unity: isospectrality, modified Q-operator and functional Bethe ansatz

We investigate an N-state spin model called quantum relativistic Toda chain and based on the unitary finite dimensional representations of the Weyl algebra with q being N-th primitive root of unity. Parameters of the finite dimensional representation of the local Weyl algebra form the classical discrete integrable system. Nontrivial dynamics of the classical counterpart corresponds to isospectral transformations of the spin system. Similarity operators are constructed with the help of modified Baxter's Q-operators. The classical counterpart of the modified Q-operator for the initial homogeneous spin chain is a Baecklund transformation. This transformation creates an extra Hirota-type soliton in a parameterization of the chain structure. Special choice of values of solitonic amplitudes yields a degeneration of spin eigenstates, leading to the quantum separation of variables, or the functional Bethe ansatz. A projector to the separated eigenstates is constructed explicitly as a product of modified Q-operators.Comment: 52 pages, LaTeX2

Yangian Algebras and Classical Riemann Problems

We investigate different Hopf algebras associated to Yang's solution of quantum Yang-Baxter equation. It is shown that for the precise definition of the algebra one needs the commutation relations for the deformed algebra of formal currents and the specialization of the Riemann problem for the currents. Two different Riemann problems are considered. They lead to the central extended Yangian double associated with ${sl}_2$ and to the degeneration of scaling limit of elliptic affine algebra. Unless the defining relations for the generating functions of the both algebras coincide their properties and the theory of infinite-dimensional representations are quite different. We discuss also the Riemann problem for twisted algebras and for scaled elliptic algebra.Comment: 36 pages, 3 figures under bezier.sty, corrected some typo

Angular Quantization of the Sine-Gordon Model at the Free Fermion Point

The goal of this paper is to analyse the method of angular quantization for the Sine-Gordon model at the free fermion point, which is one of the most investigated models of the two-dimensional integrable field theories. The angular quantization method (see hep-th/9707091) is a continuous analog of the Baxter's corner transfer matrix method. Investigating the canonical quantization of the free massive Dirac fermions in one Rindler wedge we identify this quantization with a representation of the infinite-dimensional algebra introduced in the paper q-alg/9702002 and specialized to the free fermion point. We construct further the main ingredients of the SG theory in terms of the representation theory of this algebra following the approach by M.Jimbo, T.Miwa et al.Comment: 35 pages, LaTeX 2.09, bezier.sty, final version for publicatio