  The generating functional of the cyclic representation of the CCR (Canonical
Commutation Relations) 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
non-equivalence of ensembles in the condensate region in spite of the
condensate density being zero locally.
