Low-Dimensional Models in Statistical Physics and Quantum Field Theory

1. Front Matter

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2. The chern-simons theory and quantized moduli spaces of flat connections

   • Anton Yu. Alekseev, Volker Schomerus

   Pages 1-26

3. Comments about higgs fields, noncommutative geometry, and the standard model

   • G. Cammarata, R. Coquereaux

   Pages 27-50

4. Large new applications of Bethe Ansatz

   • L. D. Faddeev

   Pages 51-70

5. University in turbulence: An exactly solvable model

   • K. Gawedzki, A. Kupiainen

   Pages 71-105

6. Introduction to integrable models of statistical physics

   • H. Grosse

   Pages 107-123

7. Yang-Baxter equation and reflection equations in integrable models

   • P. P. Kulish

   Pages 125-144

8. Scattering matrices and affine Hecke algebras

   • V. Pasquier

   Pages 145-163

9. Some algebraic and analytic structures in integrable systems

   • Nicolai Reshetikhin

   Pages 165-199

10. Monodromy representation of the mapping class group B _n for the su ₂ Knizhnik-Zamolodchikov equation

    • Yassen S. Stanev, Ivan T. Todorov

    Pages 201-222

11. What are the quantum mechanical Lyapunov exponents?

    • W. Thirring

    Pages 223-237

12. Area-preserving structure of massless matter-gravity fields in 1+1 dimensions

    • G. Amelino-Camelia, D. Bak, D. Seminara

    Pages 239-244

13. Solitons in the Calogero-Sutherland collective field model

    • I. Andrić, V. Bardek, L. Jonke

    Pages 245-248

14. W_1+∞ minimal models and the hierarchy of the quantum hall effect

    • A. Cappelli, C. A. Trugenberger, G. R. Zemba

    Pages 249-258

15. Creation and annihilation operators for b−c systems on general algebraic curves

    • F. Ferrari, J. Sobczyk

    Pages 259-263

16. Interacting electrons and localized spins: Exact results from conformal field theory

    • P. Fröjdh, H. Johannesson

    Pages 265-271

17. On the U(1)-Problem of QED2

    • Ch. Gattringer

    Pages 273-278

18. The finite Gauge model on the truncated sphere

    • H. Grosse, C. Klimčík, P. Prešnajder

    Pages 279-283

19. Local operators in massive quantum field theories

    • A. Koubek

    Pages 285-290

20. On anomalies and noncommutative geometry

    • E. Langmann

    Pages 291-297

This book contains thoroughly written reviews of modern developments in low-dimensional modelling of statistical mechanics and quantum systems. It addresses students as well as researchers. The main items can be grouped into integrable (quantum) spin systems, which lead in the continuum limit to (conformal invariant) quantum field theory models and their algebraic structures, ranging from the Yang-Baxter equation and quantum groups to noncommutative geometry.

• Chern-Simons-Theory
• Integrable Systems
• Quantum Groups
• Yang-Baxter-Equation
• statistical physics

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