On the existence of inequivalent quasi deterministic domains

In the framework of the history approach to quantum mechanics and, in particular, of the formulation of Gell-Mann and Hartle, the question of the existence of inequivalent decoherent sets of histories is reconsidered. A simple but acceptably realistic model of the dynamics of the universe is proposed and a particular set of histories is shown to be decoherent. By suitable transformations of this set, a family of sets of histories is then generated, such that the sets, first, are decoherent on the basis of the assumed dynamics of the universe and, secondly, are certainly inequivalent, apart from trivial special cases. Finally, the original set of histories is refined to get a model of the usual quasiclassical domain and it is shown, that, applying to it the previously considered transformations, a family of sets of histories is obtained which share typical properties of the usual quasiclassical domain.