J. Fr hlich, A. Knowles, A. Pizzo
Atomism and Quantization
(386K, Postscript)
ABSTRACT. 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 note 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 0 in the mean-field limit. This is a Egorov-type theorem.