Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory

ISBN-13: 9780792371847 / Angielski / Miękka / 2001 / 335 str.

S. Pakuliak; G. Von Gehlen

Opis

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Spis treści

A new basis for Bethe vectors of the Heisenberg model; T.-D. Albert, K. Ruhlig. The form factors and quantum equation of motion in the sine-Gordon model; H. Babudjian, M. Karowski. Instantons, Hilbert schemes and integrability; H.W. Braden, N.A. Nekrasov. Low-temperature behaviour of 2D lattice SU(2) spin model; O. Borisenko, V. Kushnir. Form factor representation of the correlation functions of the two dimensional Ising model on a cylinder; A.I. Bugrij. Aspects of integrable quantum field theories with boundaries; E. Corrigan. Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras; B.L. Feigin, A.V. Odesskii. Quantized moduli spaces of the bundles on the elliptic curve and their applications; B.L. Feigin, A.V. Odesskii. Thermodynamic Bethe ansatz and form factors for the homogeneous sine-Gordon models; A. Fring. The superintegrable chiral Potts quantum chain and generalized Chebyshev polynomials; G. von Gehlen, S.-S. Roan. Dualities in integrable systems: geometrical aspects; A. Gorsky, V. Rubtsov. Integrable evolutionary equations via Lie algebras on hyperelliptic curves; P. Holod, T. Skrypnyk. The quantum dilogarithm and Dehn twists in quantum Teichmüller theory; R. Kashaev. Unitary representations of the modular and two-particle q-deformed Toda chains; S. Kharchev, et al. The Algebraic Bethe Ansatz and the correlation functions of the Heisenberg magnet; N.A. Kitanine, N.A. Slavnov. Dual algebras with non-linear Posson brackets; A. Korovnichenko, A. Zhedanov. Sine-Gordon solitons vs. relativistis Calogero-Moser particles; S.N.M. Ruijsenaars. Integrable three dimensional models in wholly discrete space-time; S. Sergeev. Elliptic beta integrals andspecial functions of hypergeometric type; V.P. Spiridonov. The 9-vertex model with a special value of the crossing parameter and the related XYZ spin chain; Y. Stroganov. Correspondence between the XXZ model in roots of unity and the one-dimensional quantum Ising chain with different boundary conditions; R.A. Usmanov. Index. List of the Workshop Participants.