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

S. Pakuliak, G. von Gehlen (Herausgeber)

Buch | Hardcover

335 Seiten

2001 | 2001 ed.
Kluwer Academic Publishers (Verlag)
978-0-7923-7183-0 (ISBN)

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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.

A new basis for Bethe vectors of the Heisenberg model.- The form factors and quantum equation of motion in the sine-Gordon model.- Instantons, Hilbert schemes and integrability.- Low-temperature behaviour of 2D lattice SU(2) spin model.- Form factor representation of the correlation functions of the two dimensional Ising model on a cylinder.- Aspects of integrable quantum field theories with boundaries.- Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras.- Quantized moduli spaces of the bundles on the elliptic curve and their applications.- Thermodynamic Bethe ansatz and form factors for the homogeneous sine-Gordon models.- The superintegrable chiral Potts quantum chain and generalized Chebyshev polynomials.- Dualities in integrable systems: geometrical aspects.- hyperelliptic curves.- The quantum dilogarithm and Dehn twists in quantum Teichmüller theory.- Unitary representations of the modular and two-particle q-deformed Toda chains.- The Algebraic Bethe Ansatz and the correlation functions of the Heisenberg magnet.- Dual algebras with non-linear Poisson brackets.- Sine-Gordon solitons vs. relativistic Calogero-Moser particles.- Integrable three dimensional models in wholly discrete space-time.- Elliptic beta integrals and special functions of hypergeometric type.- The 8-vertex model with a special value of the crossing parameter and the related XYZ spin chain.- Correspondence between the XXZ model in roots of unity and the one-dimensional quantum Ising chain with different boundary conditions.- List of the Workshop Participants.

Reihe/Serie	NATO Science Series II: Mathematics, Physics and Chemistry ; 35
Zusatzinfo	VII, 335 p.
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
	Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
ISBN-10	0-7923-7183-6 / 0792371836
ISBN-13	978-0-7923-7183-0 / 9780792371830
Zustand	Neuware