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

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.

---

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.

---

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.
Content:
Front Matter....Pages i-vii
A New Basis for Bethe Vectors of the Heisenberg Model....Pages 1-16
The Form Factors and Quantum Equation of Motion in the Sine-Gordon Model....Pages 17-34
Instantons, Hilbert Schemes and Integrability....Pages 35-54
Low-Temperature Behaviour of 2D Lattice SU(2) Spin Model....Pages 55-63
Form Factor Representation of the Correlation Functions of the two Dimensional Ising Model on a Cylinder....Pages 65-93
Aspects of Integrable Quantum Field Theories with Boundaries....Pages 95-107
Functional Realization of Some Elliptic Hamiltonian Structures and Bosonization of the Corresponding Quantum Algebras....Pages 109-122
Quantized Moduli Spaces of the Bundles on the Elliptic Curve and Their Applications....Pages 123-137
Thermodynamic Bethe Ansatz and Form Factors for the Homogeneous Sine-Gordon Models....Pages 139-153
The Superintegrable Chiral Potts Quantum Chain and Generalized Chebyshev Polynomials....Pages 155-172
Dualities in Integrable Systems: Geometrical Aspects....Pages 173-198
Integrable Evolutionary Equations Via Lie Algebras on Hyperelliptic Curves....Pages 199-210
The Quantum Dilogarithm and Dehn Twists in Quantum Teichm?ller Theory....Pages 211-221
Unitary Representations of the Modular and Two-Particle Q-Deformed Toda Chains....Pages 223-242
The Algebraic Bethe Ansatz and the Correlation Functions of the Heisenberg Magnet....Pages 243-264
Dual Algebras with Non-Linear Poisson Brackets....Pages 265-272
Sine-Gordon Solitons vs. Relativistic Calogero-Moser Particles....Pages 273-292
Integrable Three Dimensional Models in Wholly Discrete Space-Time....Pages 293-304
Elliptic Beta Integrals and Special Functions of Hypergeometric Type....Pages 305-313
The 8-Vertex Model with a Special Value of the Crossing Parameter and the Related XYZ Spin Chain....Pages 315-319
Back Matter....Pages 333-335
Correspondence Between the XXZ Model in Roots of Unity and the One-Dimensional Quantum Ising Chain with Different Boundary Conditions....Pages 321-331

---

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.
Content:
Front Matter....Pages i-vii
A New Basis for Bethe Vectors of the Heisenberg Model....Pages 1-16
The Form Factors and Quantum Equation of Motion in the Sine-Gordon Model....Pages 17-34
Instantons, Hilbert Schemes and Integrability....Pages 35-54
Low-Temperature Behaviour of 2D Lattice SU(2) Spin Model....Pages 55-63
Form Factor Representation of the Correlation Functions of the two Dimensional Ising Model on a Cylinder....Pages 65-93
Aspects of Integrable Quantum Field Theories with Boundaries....Pages 95-107
Functional Realization of Some Elliptic Hamiltonian Structures and Bosonization of the Corresponding Quantum Algebras....Pages 109-122
Quantized Moduli Spaces of the Bundles on the Elliptic Curve and Their Applications....Pages 123-137
Thermodynamic Bethe Ansatz and Form Factors for the Homogeneous Sine-Gordon Models....Pages 139-153
The Superintegrable Chiral Potts Quantum Chain and Generalized Chebyshev Polynomials....Pages 155-172
Dualities in Integrable Systems: Geometrical Aspects....Pages 173-198
Integrable Evolutionary Equations Via Lie Algebras on Hyperelliptic Curves....Pages 199-210
The Quantum Dilogarithm and Dehn Twists in Quantum Teichm?ller Theory....Pages 211-221
Unitary Representations of the Modular and Two-Particle Q-Deformed Toda Chains....Pages 223-242
The Algebraic Bethe Ansatz and the Correlation Functions of the Heisenberg Magnet....Pages 243-264
Dual Algebras with Non-Linear Poisson Brackets....Pages 265-272
Sine-Gordon Solitons vs. Relativistic Calogero-Moser Particles....Pages 273-292
Integrable Three Dimensional Models in Wholly Discrete Space-Time....Pages 293-304
Elliptic Beta Integrals and Special Functions of Hypergeometric Type....Pages 305-313
The 8-Vertex Model with a Special Value of the Crossing Parameter and the Related XYZ Spin Chain....Pages 315-319
Back Matter....Pages 333-335
Correspondence Between the XXZ Model in Roots of Unity and the One-Dimensional Quantum Ising Chain with Different Boundary Conditions....Pages 321-331
....