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Introduction to Integrability
Last Updated: 2026-02-05 16:06:49
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 HS16: https://moodle-app2.let.ethz.ch/course/view.php?id=2601
Learning Materials (Links)
- Moodle course
- Moodle-Kurs / Moodle course
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Introduction to Integrability |
|
2 h weekly |
| exercise | Introduction to Integrability |
|
1 h weekly |
Offered In
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Selection: Mathematical Physics, Theoretical Physics (In the Bachelor's programme in Mathematics 402-0204-00L Electrodynamics is eligible as an elective course, but only if 402-0224-00L Theoretical Physics isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office ( ) after having received the credits.)
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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