The classical limit of a state on the Weyl algebra

Abstract

This paper considers states on the Weyl algebra of the canonical commutation relations over the phase space R2n. We show that a state is regular if and only if its classical limit is a countably additive Borel probability measure on R2n. It follows that one can “reduce” the state space of the Weyl algebra by altering the collection of quantum mechanical observables so that all states are ones whose classical limit is physical.