Bounds on exponentials of local number operators in quantum statistical mechanics

We consider the quantum systems of interacting Bose particles confined to a bounded region of the configuration spaces ^v . For a class of superstable interactions we obtain bounds on exponentials of local number operators for any temperature and activity. The method we use is the Wiener integral formalism in statistical mechanics. As a consequence any thermodynamic limit states are entire analytic and locally normal in the CCR algebra. In some cases these are modular states.Research supported in part by a grant from Korean Science Foundation