\(W^*\)-dynamics of infinite quantum systems (Q794241)

Let \({\mathcal A}\) be a \(C^*\)-algebra of local observables corresponding to the space \({\mathbb{R}}^{\iota}\) or \({\mathbb{Z}}^{\iota}\), \({\mathcal F}\) a set of certain states on \({\mathcal A}\) and \(\tau\) a one-parameter group of affine transformations of \({\mathcal F}\). The author proves that in the case when the pair (\({\mathcal F},\tau)\) forms a physical folium in the sense of a former paper of his [Proc. Symp. Pure Math. 38, Part 2, Kingston/Ont. 1982, 491-497 (1982; Zbl 0528.46055)], then the dynamics \(\tau\) is associated to a group of *-automorphisms of a \(W^*\)-algebra which is the dual for \({\mathcal F}\). This situation includes some particular cases considered by R. F. Streater, D. W. Robinson, O. Bratteli, D. A. Dubin and the author.