J Fröhlich et al 2007 J. Phys. A: Math. Theor. 40 3033 doi:10.1088/1751-8113/40/12/S09
J Fröhlich, A Knowles and A Pizzo
Show affiliationsWithin 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.
81Sxx General quantum mechanics and problems of quantization
Quantum gases, liquids and solids
Issue 12 (23 March 2007)
Received 7 September 2006, in final form 13 November 2006
Published 7 March 2007
J Fröhlich et al 2007 J. Phys. A: Math. Theor. 40 3033
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