Atomism and Quantization∗

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. This is a slightly modified version of an article published in J. Phys. A 40, 3033-3045, 2007. [email protected] [email protected] [email protected]