On the exact mean-field description of continuous quantum systems in equilibrium II

The thermodynamic limit of free energy density of continuous quantum systems with bounded separable 2-body interactions, confined to a compact Riemann space, is investigated. It is shown that such systems, similarly as n-particle quantum systems in a bounded region in Rv, which were discussed in an earlier article, can be exactly described in this limit as noninteracting systems subject to a mean field, equal to the averaged 2-body interaction. The form of equations for the mean field depends on the statistics obeyed by the particles. Conditions for the values of inverse temperature, at which the mean-field description may be invalid, are derived. As an application of the method, a system of coupled oscillators on a sphere in Rv is investigated.