Ammari, Zied; Nier, Francis Mean field limit for bosons and infinite dimensional phase-space analysis. (English) Zbl 1171.81014 Ann. Henri Poincaré 9, No. 8, 1503-1574 (2008). 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. Reviewer: Michael B. Mensky (Moskva) Cited in 4 ReviewsCited in 67 Documents 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 Keywords:Bosonic quantum field; Wigner measure; Mean field dynamics × Cite Format Result Cite Review PDF Full Text: DOI arXiv