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402-0822-13L 6 Credits BSC , MSC D-PHYS , D-MATH

Introduction to Integrability

Lecturers & Examiners: Prof. Dr. Niklas Beisert
VVZ CR n/a

Last Updated: 2026-02-05 16:29:44

Abstract

This course gives an introduction to the theory of integrable systems, related symmetry algebras and efficients calculational methods.

Objective

Integrable systems are a special class of physical models that can be solved exactly due to an exceptionally 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 introduce the notion and formulation of integrability in classical and quantum mechanics. We discuss various efficient methods for constructing solutions and eigenstates in these models. Finally, we elaborate on the enhanced symmetries that underly integrable models.

Content

• Classical Integrability • Algebraic Methods for Integrability • Classical Spin Chains • Spectral Curves and Inverse Scattering • Quantum Spin Chains • Bethe Ansatz • Classical and Quantum Algebra

Resources

Literature

• V. Chari, A. Pressley, "A Guide to Quantum Groups", Cambridge University Press (1995) • O. Babelon, D. Bernard, M. Talon, "Introduction to Classical Integrable Systems", Cambridge University Press (2003) • N. Reshetikhin, "Lectures on the integrability of the 6-vertex model", http://arxiv.org/abs/1010.5031 • L.D. Faddeev, "How Algebraic Bethe Ansatz Works for Integrable Model", http://arxiv.org/abs/hep-th/9605187 * D. Bernard, "An Introduction to Yangian Symmetries", Int. J. Mod. Phys. B7, 3517-3530 (1993), http://arxiv.org/abs/hep-th/9211133 * V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, "Quantum Inverse Scattering Method and Correlation Functions", Cambridge University Press (1997) • C. Gómez, M. Ruiz-Altaba, G. Sierra, "Quantum Groups In Two-Dimensional Physics", Cambridge University Press (1996) • L. D. Faddeev, L. A. Takhtajan, "Hamiltonian Methods in the Theory of Solitons", Springer (2007) • Lecture of HS23: https://moodle-app2.let.ethz.ch/course/view.php?id=21116

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC

Examination

Type
session examination
Mode
oral 25 minutes
Actual duration of each oral exam is 20 minutes (25 minutes for purposes of exam schduliung)

Course Components

Type Title Time & Place Hours
lecture Introduction to Integrability
  • Thu 13:45-15:30 (HIT F 31.2)
2 h weekly
exercise Introduction to Integrability
Starts in the second week of the semester. Every other week.
  • Thu 15:45-17:30 (HIT F 31.2)
1 h weekly

Offered In