Solitons and two-dimensional integrable models

2010 ◽  
pp. 79-130
Author(s):  
Yitzhak Frishman ◽  
Jacob Sonnenschein
Keyword(s):  
Integrable Models ◽  
Two Dimensional

S-matrix Theory

2020 ◽  
pp. 622-675
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Matrix Theory ◽  
Point Of View ◽  
Integrable Models ◽  
Geometrical Interpretation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Recursive Structure ◽  
Mathematical Point ◽  
S Matrix ◽  
Dynamical Principle

Chapter 17 discusses the S-matrix theory of two-dimensional integrable models. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial features that lead to important simplifications of the formalism and its successful application. This chapter deals with the analytic theory of the S-matrix of the integrable models. A particular emphasis is put on the dynamical principle of bootstrap, which gives rise to a recursive structure of the amplitudes. It also covers several dynamical quantities, such as mass ratios or three-coupling constants, which have an elegant mathematic formulation that is also of easy geometrical interpretation.

FROM INHOMOGENEOUS SIX-VERTEX LATTICE MODELS TO CONTINUUM QUANTUM INTEGRABLE MODELS

1992 ◽  
Vol 07 (25) ◽  
pp. 6385-6403
Author(s):  
Y.K. ZHOU
Keyword(s):  
Integrable Systems ◽  
Scaling Limit ◽  
Lattice Models ◽  
Integrable Models ◽  
Two Dimensional ◽  
Vertex Model ◽  
Quantum Integrable Systems ◽  
Vertex Models ◽  
Quantum Integrable Models ◽  
Sine Gordon Model

A method to find continuum quantum integrable systems from two-dimensional vertex models is presented. We explain the method with the example where the quantum sine-Gordon model is obtained from an inhomogeneous six-vertex model in its scaling limit. We also show that the method can be applied to other models.

scholarly journals Integrable models and degenerate horizons in two-dimensional gravity

1999 ◽  
Vol 61 (2) ◽  
Author(s):  
J. Cruz ◽  
A. Fabbri ◽  
D. J. Navarro ◽  
J. Navarro-Salas
Keyword(s):  
Integrable Models ◽  
Two Dimensional ◽  
Dimensional Gravity

scholarly journals GELFAND–DICKEY ALGEBRA AND HIGHER SPIN SYMMETRIES ON T2 = S1 × S1

2008 ◽  
Vol 23 (31) ◽  
pp. 5059-5080
Author(s):  
M. B. SEDRA
Keyword(s):  
Integrable Models ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Dimensional Torus ◽  
Conformal Field ◽  
Generalized Symmetries ◽  
Higher Spin

In this work we aim to renew the interest in higher conformal spins symmetries and their relations to quantum field theories and integrable models. We consider the extension of the conformal Frappat et al. symmetries containing the Virasoro and the Antoniadis et al. algebras as particular cases describing geometrically special diffeomorphisms of the two-dimensional torus T2. We show explicitly, in a consistent way, how one can extract these generalized symmetries from the Gelfand–Dickey algebra. The link with Liouville and Toda conformal field theories is established and various important properties are discussed.

scholarly journals MICZ-Kepler systems in noncommutative space and duality of force laws

2014 ◽  
Vol 29 (32) ◽  
pp. 1450187 ◽  
Author(s):  
Partha Guha ◽  
E. Harikumar ◽  
N. S. Zuhair
Keyword(s):  
Deformation Parameter ◽  
Kepler Problem ◽  
Space Time ◽  
Integrable Models ◽  
Noncommutative Space ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Sundman Transformation ◽  
Two Systems ◽  
Commutative Space

In this paper, we analyze the modification of integrable models in the κ-deformed space–time. We show that two-dimensional isotropic oscillator problem, Kepler problem and MICZ-Kepler problem in κ-deformed space–time admit integrals of motion as in the commutative space. We also show that the duality equivalence between κ-deformed Kepler problem and κ-deformed two-dimensional isotropic oscillator explicitly, by deriving Bohlin–Sundman transformation which maps these two systems. These results are valid to all orders in the deformation parameter.

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