CiNii Books - Symétries quantiques : Les Houches, session LXIV, 1 août

One of the greatest challenges that theoretical physics faces at the end of the century is to blend together the two revolutions of the beginning of the century, namely general relativity and quantum mechanics. One message that has become clear from the start and is common to both revolutions is that there is no limit to the level of sophistication of mathematics that will become essential to physics. This book comprises the lecture notes of the 1995 Les Houches Summer School. The aim of the school was to cover a wide range of areas, from theoretical physics to abstract mathematics, that are relevant in the search of a quantum theory of gravity. The lectures provide a systematic introduction to topological and conformal field theories, supersymmetry and super Yang-Mills theories, string theory and superstring dualities, integrable lattice models and quantum groups, non commutative geometry and the theory of diffeomorphism groups.It is directed at graduate students and researchers in theoretical physics and mathematics.

Table of Contents

Preface. Part 1 - Mathematics. Courses: 1. Fields, Strings and Duality (R. Dijkgraaf). 2. How the algebraic Bethe Ansatz works for integrable models (L.D. Faddeev). 3. Supersymmetric quantum theory, non-commutative geometry and gravitation (J. Froehlichet al.). 4. Lectures on the quantum geometry of string theory (B.R. Greene). 5. Symmetry approach to the XXZ model (T. Miwa). Seminars: 1. Superstring dualities, Dirichlet Branes and the small scale structure of space (M. Douglas). 2. Testing the standard model and beyond (J. Ellis). 3. Quantum group approach to strongly coupled two dimensional gravity (J.-L. Gervais). 4. N=2 Superalgebra and non-commutative geometry (H. Grosse et al.). 5. Lecture on N=2 supersymmetric gauge theory (W. Lerche). Part 2 - Physics. Courses: 6. Noncommutative geometry: the spectral aspect (A. Connes). 7.The KZB equations on Riemann surfaces (G. Felder). 8. From diffeomorphism groups to loop spaces via cyclic homology (J.-L. Loday). 9. Quantum groups and braid groups (M. Rosso). 10. From index theory to non commutative geometry (N. Teleman). 11. Compact quantum groups (S.L. Woronowicz). Seminars: 6. Seiberg-Witten invariants and vortex equations (O. Garcia-Prada). 7. Quantization of Poisson algebraic groups and Poisson homogeneous spaces (P. Etingof and D. Kazhdan). 8. Eta and Torsion (J. Lott). 9. Symplectic formalism in conformal field theory (A. Schwarz). 10. Quantization of geometry associated to the quantized Knizhnik-Zamolodchikov equations (A. Varchenko).

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Symétries quantiques : Les Houches, session LXIV, 1 août - 8 septembre 1995 Quantum symmetries

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