Introduction to Classical and Quantum Integrability - Département de Physique de l'Ecole Normale supérieure

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Introduction to Classical and Quantum Integrability

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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Next student seminar :
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Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Faculty: Vladimir Kazakov
ECTS: 3
Language of instruction: English
Exam: Writing an individual project then oral presentation (with questions) made remotely.
Key words : spin chains, integrability , field theories, PDE

Plan of lecture

1. Examples of integrable classical and quantum systems (degeneracy of spectrum of hydrogen atom, Kepler orbits, KAM theory, Hopf-Burgers equation, Calogero system)
2. Classical integrability: Lax pair, integrals of motion, construction of soliton solutions on the example of Korteweg-deVries (KdV) integrable hierarchy of PDE’s; Other examples of integrable many-body systems and field theories (KdV, Toda, non-linear Schrodinger, sigma-models)
3. Quantum integrability. Bosons in one dimension with delta interaction: equivalence to non-linear Schrödinger equation; Lieb-Liniger theory; Thermodynamical Bethe ansatz (TBA)
4. Quantum Heisenberg spin chain: solution by Bethe ansatz, Baxter equation, energy spectrum
5. Alternative methods for quantum spin chains: R-matrix, algebraic Bethe ansatz
6. Advanced subjects (if time permits): Spin chains with gl(N) symmetry; Integrable QFTs in 2d (sigma models); S matrix bootstrap, Integrability and AdS/CFT correspondence

Wednesday at 09:00am - Room L361, third floor ENS Physics department -: 13,20,27/01; 3,10,17/02; 3,10,17/03; exam: 31/03, 2021

Quick links

Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr