Within the framework of the theory of interacting classical and quantum gases, it is shown that the atomistic constitution of gases can be understood as a consequence of (second) quantization of a continuum theory of gases. In this paper, this is explained in some detail for the theory of non-relativistic interacting Bose gases, which can be viewed as the second quantization of a continuum theory whose dynamics is given by the Hartree equation. Conversely, the Hartree equation emerges from the theory of Bose gases in the mean-field limit. It is shown that, for such systems, the time evolution of 'observables' commutes with their Wick quantization, up to quantum corrections that tend to zero in the mean-field limit. This is an Egorov-type theorem.
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Fröhlich et al. (2007) studied this question.