School of 2020

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Twentysixth School: Heigenbrücken,

funded by the Wilhelm and Else Heraeus Foundation


Lecture Program:

Gleb Arutyunov
Integrable systems — from classics to AdS/CFT
Dorothea Bahns
Perturbative algebraic quantum field theory
Daniele Dorigoni
Resurgence in quantum field theory
Marc Henneaux
(Brussels, Paris)
Chern-Simons theory and 3D gravity
(cancelled because of corona, postponed to 2021)
Ivo Sachs
BV quantization and string field theory

The instruction language is English.
Some lecture notes may appear later and will be made available here

Recommended Literature: (to be provided)

  • Arutyunov:
    1. O. Babelon, D. Bernard, and M. Talon, Introduction to classical integrable systems, Cambridge University Press, 2003.
    2. B. Sutherland, Beautiful Models: 70 Years of Exactly Solved Quantum Many-body Problems, World Scientific, 381 p., 2004.
    3. C.N. Yang, Some exact results for the many body problems in one dimension with repulsive delta function interaction,
    Phys. Rev. Lett., 19:1312–1314, 1967.   
    4.  A.B. Zamolodchikov and Al.B. Zamolodchikov, Factorized S Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models. Annals Phys., 120:253–291, 1979.
    5. H.B. Thacker, Exact integrability in quantum field theory and statistical systems, Rev. Mod. Phys., 53:253–285, 1981.
    6. L. D. Faddeev, How Algebraic Bethe Ansatz works for integrable model,  Les-Houches lectures, arXiv:hep-th/9605187.
    7. M. Gaudin, The Bethe Wavefunction, Translated from French original `La fonction d'onde de Bethe' (1983) by J.-S. Caux, Cambridge University Press, 2014.
    8. G. Arutyunov, Elements of classical and quantum integrable systems, Springer, 2019.
  • Bahns:
    1. M. Dütsch, “From Classical Field Theory to Perturbative Quantum Field Theory”, Birkhäuser 2019
    K. Rejzner, “Perturbative Algebraic Quantum Field Theory — An Introduction for Mathematicians”, Springer 2016
  • Dorigoni:
    1. D. Dorigoni: 'An Introduction to Resurgence, Trans-Series and Alien Calculus' 1411.3585
    2. I. Aniceto, G. Başar, R. Schiappa: 'A Primer on Resurgent Transseries and Their Asymptotics' 1802.10441
    3. M. Marino, ‘Lectures on non-perturbative effects in large N gauge theories, matrix models and strings’, 1206.6272
  • Sachs:
    For BV: S. Weinberg “The Quantum Theory of Fields”, Vol. 2
    J. Gomis, J. Paris and S. Samuel, “Antibracket, antifields and gauge theory quantization”, hep-th/9412228
    For String theory: J. Polchisnki, “String Theory”, Vol. 1