Low-Dimensional Models in Statistical Physics and Quantum Field Theory: Proceedings of the 34. Internationale Universitätswochen für Kern- und Teilchenphysik Schladming, Austria, March 4–11, 1995

Anton Yu. Alekseev, Volker Schomerus (auth.), Harald Grosse, Ludwig Pittner (eds.)3540609903, 9783540609902

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.

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Table of contents :
The chern-simons theory and quantized moduli spaces of flat connections….Pages 1-26
Comments about higgs fields, noncommutative geometry, and the standard model….Pages 27-50
Large new applications of Bethe Ansatz….Pages 51-70
University in turbulence: An exactly solvable model….Pages 71-105
Introduction to integrable models of statistical physics….Pages 107-123
Yang-Baxter equation and reflection equations in integrable models….Pages 125-144
Scattering matrices and affine Hecke algebras….Pages 145-163
Some algebraic and analytic structures in integrable systems….Pages 165-199
Monodromy representation of the mapping class group B n for the su 2 Knizhnik-Zamolodchikov equation….Pages 201-222
What are the quantum mechanical Lyapunov exponents?….Pages 223-237
Area-preserving structure of massless matter-gravity fields in 1+1 dimensions….Pages 239-244
Solitons in the Calogero-Sutherland collective field model….Pages 245-248
W 1+∞ minimal models and the hierarchy of the quantum hall effect….Pages 249-258
Creation and annihilation operators for b−c systems on general algebraic curves….Pages 259-263
Interacting electrons and localized spins: Exact results from conformal field theory….Pages 265-271
On the U(1)-Problem of QED 2 ….Pages 273-278
The finite Gauge model on the truncated sphere….Pages 279-283
Local operators in massive quantum field theories….Pages 285-290
On anomalies and noncommutative geometry….Pages 291-297
Quantum deformations of space-time symmetries with fundamental mass parameter….Pages 299-303
Magnetic field-induced 2D wigner solid versus incompressible quantum liquid….Pages 305-308
Random Walks over Wilson loop space….Pages 309-314
Polynomial identities on Reflection Equation Algebra….Pages 315-320
Introduction to Poisson σ-models….Pages 321-333
On solution of self-duality equation in quantum-group Gauge theory….Pages 335-339