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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NATO Science Series B:http://image.papertrans.cn/q/image/781200.jpg

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Non-Commutative Gauge Fields from Quantum GroupsWe give a non-technical introduction into the theory of non-commutative lattice gauge fields with quantum gauge group. The general construction is illustrated at the example of the Hamiltonian Chern-Simons theory. We also review the counterpart of the Noether’s theorem for quantum groups.

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濃縮

Quantum Integrable Models on 1 + 1 Discrete Space TimeClassical theory of solitons was based on two main examples: the KdV equation [1] and Toda lattice [2]. The role of continuous space variable . in the first example is played by discrete integer valued variable . in the second one. So discrete space was not foreign to the soliton theory from its very beginning.

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Turbulence under a Magnifying GlassThis is an introductory course on the open problems of fully developed turbulence which present a long standing challenge for theoretical and mathematical physics. The plan of the course is as follows:

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Exercises in Equivariant CohomologyEquivariant cohomology [1]–[5] is at the core of the geometrical interpretation of the topological -more precisely, cohomological- field theories proposed by E. Witten in 1988 [6, 7]. The corresponding mathematical equipment also sheds some light on the gauge fixing procedure [8] familiar in the Lagrangian formulation of gauge theories.

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