3 research outputs found
Introduction to Quantum Integrability
In this article we review the basic concepts regarding quantum integrability.
Special emphasis is given on the algebraic content of integrable models. The
associated algebras are essentially described by the Yang-Baxter and boundary
Yang-Baxter equations depending on the choice of boundary conditions. The
relation between the aforementioned equations and the braid group is briefly
discussed. A short review on quantum groups as well as the quantum inverse
scattering method (algebraic Bethe ansatz) is also presented.Comment: 56 pages, Latex. A few typos correcte
Selected Topics in Classical Integrability
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.Comment: 40 pages, Latex. A few typos correcte