We prove that the dynamics of an infinite quantum system, as formulated in the Schr6dinger representation within the framework constructed in an earlier work [1 ], corresponds to *-automorphisms of the W*-algebra dual to the space of its physical states.
The dynamics of infmite quantum systems is generally taken to be given by some appropriate limit of that of corresponding finite ones [ 1 ] -[9]. Accordingly, it has been established, with the C*-algebraic formulation of quantum theory, that in the simplest ones, e.g., lattice systems with t'mite range forces, the dynamics corresponds to automorphisms of the observables [10], [11] ; while, more generally, this is not so [3 ] -[5 ], [9 ], [ 12 ], [ 13 ], and time-translations in the island ~ of a Gibbs state correspond in some cases to automorphisms [3], [4], [9], in others to nonautomorphic isomorphisms [13], of the weak closure of the associated GNS representation of the algebra of observables.
The object of the present note is to show that the dynamics of an infinite quantum system, as formulated in the SchrSdinger representational framework that we constructed some time ago