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402-0822-13L  Introduction to Integrability

SemesterHerbstsemester 2016
DozierendeN. Beisert
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch


KurzbeschreibungThis course gives an introduction to the theory of integrable systems, related symmetry algebras and efficients calculational methods.
LernzielIntegrable 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 various notions of integrability in classical mechanics, quantum mechanics and quantum field theory. We discuss efficient methods for solving such models as well as the underlying enhanced symmetries.
Inhalt* Classical Integrability
* Integrable Field Theory
* Integrable Spin Chains
* Quantum Integrability
* Integrable Statistical Mechanics
* Quantum Algebra
* Bethe Ansatz and Related Methods
* AdS/CFT Integrability
Literatur* 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)