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Mean field limit for bosons and infinite dimensional phase-space analysis. (English) Zbl 1171.81014

The infinite dimensional bosonic quantum field theory is reviewed and some new results are obtained. In particular, the construction of Wigner measures in such a theory is proposed. The application of the results to the derivation of the mean field dynamics considered. Once these asymptotic objects are well defined, it is shown how they can be used to make connections between different kinds of results or to prove new ones.

MSC:

81T08 Constructive quantum field theory
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81T70 Quantization in field theory; cohomological methods
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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