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Titlebook: Quantum Fields and Quantum Space Time; Gerard ’t Hooft,Arthur Jaffe,Raymond Stora Book 1997 Springer Science+Business Media New York 1997

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Integrable Classical and Quantum Gravitylling symmetries which effectively eliminate the dependence on all but two space-time coordinates allows us to cast the models into the form of 2. non-linear (./.)-coset space σ-models coupled to gravity and a dilaton. This construction includes a variety of models described by different coset space
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Quantum Affine Algebras and Integrable Quantum Systemszable Kac-Moody algebra .. Usually, the deformation parameter . is taken to be a non-zero complex number, and one thinks of ..(.) as a family of Hopf algebras over ℂ ‘depending’ on . If . = 1, one recovers the classical universal enveloping algebra of .. But one can also work ‘universally’, by regar
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Disorder Operators, Quantum Doubles, and Haag Duality in 1 + 1 Dimensionson of its relevance to two dimensional quantum field theory. The quantum double appears implicitly in the work [3] on orbifold constructions in conformai field theory, where conformal quantum field theories (CQFTs) are considered whose operators are fixpoints under the action of a symmetry group on
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Book 1997 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 qu
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Supersymmetry and Non-Commutative Geometrys and notions of differential geometry emerge from concepts and notions of the quantum theory of non-relativistic particles with spin, and how the classification of different types of differential geometry follows the classification of supersymmetries. One of our motivations is to construct some mathematical tools useful in quantum gravity.
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978-1-4899-1803-1Springer Science+Business Media New York 1997
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