Journal of mathematical physics vol:45 issue:4 pages:1606-1622
The generating functional of the cyclic representation of the canonical commutation relations (CCR) representation for the thermodynamic limit of the grand canonical ensemble of the free Bose gas with attractive boundary conditions is rigorously computed. We use it to study the condensate localization as a function of the homothety point for the thermodynamic limit using a sequence of growing convex containers. The Kac function is explicitly obtained proving nonequivalence of ensembles in the condensate region in spite of the condensate density being zero locally. (C) 2004 American Institute of Physics.