SELECTED TOPICS IN CLASSICAL INTEGRABILITY

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 ar...

Lectures on Classical Integrability

We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of

Classical Open String Integrability

We present a simple procedure to construct non-local conserved charges for classical open strings on coset spaces. This is done by including suitable reflection matrices on the classical transfer matrix. The reflection matrices must obey certain conditions for the charges to be conserved and in involution. We then study bosonic open strings on AdS5×S. We consider boundary conditions correspondi...

Classical and Quantum Integrability

It is a well-known problem to decide if a classical hamiltonian system that is integrable, in the Liouville sense, can be quantised to a quantum integrable system. We identify the obstructions to do so, and show that the obstructions vanish under certain conditions. 2000 Math. Subj. Class. 81S10.

Selected Topics in Medical Genetics