Ebook: Quantum Fields and Quantum Space Time

The 1996 NATO Advanced Study Institute (ASI) followed the international tradi­ tion of the schools held in Cargese in 1976, 1979, 1983, 1987 and 1991. Impressive progress in quantum field theory had been made since the last school in 1991. Much of it is connected with the interplay of quantum theory and the structure of space time, including canonical gravity, black holes, string theory, application of noncommutative differential geometry, and quantum symmetries. In addition there had recently been important advances in quantum field theory which exploited the electromagnetic duality in certain supersymmetric gauge theories. The school reviewed these developments. Lectures were included to explain how the "monopole equations" of Seiberg and Witten can be exploited. They were presented by E. Rabinovici, and supplemented by an extra 2 hours of lectures by A. Bilal. Both the N = 1 and N = 2 supersymmetric Yang Mills theory and resulting equivalences between field theories with different gauge group were discussed in detail. There are several roads to quantum space time and a unification of quantum theory and gravity. There is increasing evidence that canonical gravity might be a consistent theory after all when treated in. a nonperturbative fashion. H. Nicolai presented a series of introductory lectures. He dealt in detail with an integrable model which is obtained by dimensional reduction in the presence of a symmetry.

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Content:
Front Matter....Pages i-viii
Non-Commutative Gauge Fields from Quantum Groups....Pages 1-19
Duality in N = 2 SUSY SU(2) Yang-Mills Theory: A Pedagogical Introduction....Pages 21-43
Noncommutative Differential Geometry and the Structure of Space Time....Pages 45-72
Quantum Integrable Models on 1 + 1 Discrete Space Time....Pages 73-91
Supersymmetry and Non-Commutative Geometry....Pages 93-121
Turbulence under a Magnifying Glass....Pages 123-150
Quantization of Space and Time in 3 and in 4 Space-Time Dimensions....Pages 151-163
Pushing Einstein’s Principles to the Extreme....Pages 165-201
Integrable Classical and Quantum Gravity....Pages 203-243
Quantum Affine Algebras and Integrable Quantum Systems....Pages 245-263
Exercises in Equivariant Cohomology....Pages 265-279
Some Complex Quantum Manifolds and their Geometry....Pages 281-322
T-Duality and the Moment Map....Pages 323-329
Symmetries of Dimensionally Reduced String Effective Action....Pages 331-338
Non Local Observables and Confinement in BF Formulation of Yang-Mills Theory....Pages 339-348
Disorder Operators, Quantum Doubles, and Haag Duality in 1 + 1 Dimensions....Pages 349-356
The Cohomology and Homology of Quantum Field Theory....Pages 357-368
Back Matter....Pages 369-373

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Content:
Front Matter....Pages i-viii
Non-Commutative Gauge Fields from Quantum Groups....Pages 1-19
Duality in N = 2 SUSY SU(2) Yang-Mills Theory: A Pedagogical Introduction....Pages 21-43
Noncommutative Differential Geometry and the Structure of Space Time....Pages 45-72
Quantum Integrable Models on 1 + 1 Discrete Space Time....Pages 73-91
Supersymmetry and Non-Commutative Geometry....Pages 93-121
Turbulence under a Magnifying Glass....Pages 123-150
Quantization of Space and Time in 3 and in 4 Space-Time Dimensions....Pages 151-163
Pushing Einstein’s Principles to the Extreme....Pages 165-201
Integrable Classical and Quantum Gravity....Pages 203-243
Quantum Affine Algebras and Integrable Quantum Systems....Pages 245-263
Exercises in Equivariant Cohomology....Pages 265-279
Some Complex Quantum Manifolds and their Geometry....Pages 281-322
T-Duality and the Moment Map....Pages 323-329
Symmetries of Dimensionally Reduced String Effective Action....Pages 331-338
Non Local Observables and Confinement in BF Formulation of Yang-Mills Theory....Pages 339-348
Disorder Operators, Quantum Doubles, and Haag Duality in 1 + 1 Dimensions....Pages 349-356
The Cohomology and Homology of Quantum Field Theory....Pages 357-368
Back Matter....Pages 369-373
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