Introduction to Integrability – FS 2013

Description

Integrable systems are a special class of physical models that can be solved exactly due to a large number of symmetries. Examples of integrable models appear in many different areas of physics, including classical mechanics, condensed matter, 2d quantum field theories and lately in string- and gauge theories. They offer a unique opportunity to gain a deeper understanding of generic phenomena in a simplified, exactly solvable setting. In this course we shall walk the students through the various notions of integrability starting from classical mechanics and ending with quantum field theories.

Content

1. Integrability in Classical Mechanics
2. Integrable Classical Field Theory
3. Spin Chains
4. Bethe Ansatz
5. Integrable Quantum Field Theory

Literature

• G. Arutyunov, Classical and Quantum Integrable Systems,
  http://www.staff.science.uu.nl/%7earuty101/StudentSeminar.pdf
• L. Faddeev, How algebraic Bethe Ansatz works for integrable model,
  http://arxiv.org/pdf/hep-th/9605187
• V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, CUP (1997)
• O. Babelon, D. Bernard, M. Talon, Introduction to Classical Integrable Systems
• P. Dorey, Exact S-matrices, hep-th/9810026
• Z. Bajnok, L. Samaj, INTRODUCTION TO INTEGRABLE MANY-BODY SYSTEMS III

Credit Requirements

• 20 minute oral examination

Materials

Lecture Notes

• Classical Field Theory (CFT, 310 kB)
• Classical Mechanics (PDF, 278 kB)
• Spin Chains (SPINCHAINS, 265 kB)

Problem Sets

• Problem Set 1 (PDF, 132 kB)
• Problem Set XXZ (PDF, 125 kB)