Quantum statistical mechanics for superstable interactions: Bose-Einstein statistics

We study quantum systems of interacting Bose particles confined to a bounded region ofR ^v . For any superstable and (strong) lower regular interaction, we obtain uniform bounds on the expectations of exponentials of local number operators for any activity and for any temperature. The method we use here is an improvement over our previous method on the same subject. As a consequence of the bounds, any infinite volume limit states are entire analytic and locally normal. Furthermore under an integrability condition on the interaction, the limit states are modular states. In this case, we use the Green's function method to construct an infinite volume limit Hilbert spece, a strongly continuous time evolution group of unitary operators and an invariant vector. Moreover we prove the existence of the pressure and its independence of boundary conditions.