Time Translations in the Algebraic Formulation of Statistical Mechanics

Abstract

We present a new description of time translations in the C*‐algebraic formulation of statistical mechanics. This description is based on weaker assumptions than the hitherto accepted ones, due to Haag, Hugenholtz, and Winnink (HHW) [Commun. Math. Phys. 5, 215 (1967)]. It is shown that these weaker assumptions still lead to the principal results of HHW for Gibbs states and, further, that our assumptions, unlike those of HHW, are valid for the ideal Bose gas and strong‐coupling BCS models.