scholarly journals QUANTUM GROUP SYMMETRY OF INTEGRABLE SYSTEMS WITH OR WITHOUT BOUNDARY

2002 ◽  
Vol 17 (25) ◽  
pp. 3649-3661 ◽  
Author(s):  
E. RAGOUCY
Keyword(s):  
Quantum Group ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Group Symmetry ◽  
Integrals Of Motion ◽  
R Matrix ◽  
Explicit Expressions

We present a construction of integrable hierarchies without or with boundary, starting from a single R-matrix, or equivalently from a ZF algebra. We give explicit expressions for the Hamiltonians and the integrals of motion of the hierarchy in term of the ZF algebra. In the case without boundary, the integrals of motion form a quantum group, while in the case with boundary they form a Hopf coideal subalgebra of the quantum group.

scholarly journals SELECTED TOPICS IN CLASSICAL INTEGRABILITY

2012 ◽  
Vol 27 (05) ◽  
pp. 1230003 ◽  
Author(s):  
ANASTASIA DOIKOU
Keyword(s):  
Integrable Systems ◽  
Toda Chain ◽  
Lax Pair ◽  
Integrable Models ◽  
Integrals Of Motion ◽  
Curvature Condition ◽  
R Matrix ◽  
Zero Curvature ◽  
Algebraic Description ◽  
Classical Integrable

Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete and continuum classical integrable models is introduced. Using this framework the associated classical integrals of motion and the corresponding Lax pair are extracted based on algebraic considerations. Our attention is restricted to classical discrete and continuum integrable systems with periodic boundary conditions. Typical examples of discrete (Toda chain, discrete NLS model) and continuum integrable models (NLS, sine–Gordon models and affine Toda field theories) are also discussed.

scholarly journals Universal R-matrix and functional relations

2014 ◽  
Vol 26 (06) ◽  
pp. 1430005 ◽  
Author(s):  
Herman Boos ◽  
Frank Göhmann ◽  
Andreas Klümper ◽  
Khazret S. Nirov ◽  
Alexander V. Razumov
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Integrable Systems ◽  
Vertex Model ◽  
Quantum Space ◽  
R Matrix ◽  
Functional Relations

We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group [Formula: see text] related to the six-vertex model. We prove the full set of the functional relations in the form independent of the representation of the quantum group in the quantum space and specialize them to the case of the six-vertex model.

Exact S-Matrices

2020 ◽  
pp. 676-743
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Quantum Group ◽  
Scattering Theory ◽  
Integrable Model ◽  
Group Symmetry ◽  
Fusion Rules ◽  
Lee Model ◽  
Sine Gordon Model ◽  
Multiple Poles

The Ising model in a magnetic field is one of the most beautiful examples of an integrable model. This chapter presents its exact S-matrix and the exact spectrum of its excitations, which consist of eight particles of different masses. Similarly, it discusses the exact scattering theory behind the thermal deformation of the tricritical Ising model and the unusual features of the exact S-matrix of the non-unitary Yang–Lee model. Other examples are provided by O(n) invariant models, including the important Sine–Gordon model. It also discusses multiple poles, magnetic deformation, the E 8 Toda theory, bootstrap fusion rules, non-relativistic limits and quantum group symmetry of the Sine–Gordon model.

scholarly journals Exact S-matrices with affine quantum group symmetry

1995 ◽  
Vol 451 (1-2) ◽  
pp. 445-465 ◽  
Author(s):  
G.W. Delius
Keyword(s):  
Quantum Group ◽  
Group Symmetry
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