Decoherence: A dynamical approach to superselection rules?

Abstract

It is well known that the dynamical mechanism of decoherence may cause apparent superselection rules, like that of molecular chirality. These `environment-induced' or `soft' superselection rules may be contrasted with `hard' superselection rules, like that of electric charge, whose existence is usually rigorously demonstrated by means of certain symmetry principles. We address the question of whether this distinction between `hard' and `soft' is well founded and argue that, despite first appearance, it might not be. For this we give a detailed and somewhat pedagogical exposition of the basic structural properties of the spaces of states and observables in order to establish a fairly precise notion of superselection rules. We then discuss two examples: the Bargmann superselection rule for overall mass in ordinary quantum mechanics, and the superselection rule for charge in quantum electrodynamics.