Z. Ammari, F. Nier
Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
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ABSTRACT. Contrary to the finite dimensional case, Weyl and Wick quantizations
are no more asymptotically equivalent in the infinite dimensional
bosonic second quantization. Moreover neither the Weyl calculus defined
for cylindrical symbols nor the Wick calculus defined for polynomials
are preserved by the action of a nonlinear flow. Nevertheless taking
advantage carefully of the information
brought by these two calculuses in the mean field asymptotics, the
propagation of Wigner measures for general states can be proved,
extending to the infinite dimensional case a standard result of
semiclassical analysis.