A Note on the Type of Local von Neumann Algebras in Quantum Field Theory over Curved Space‐time

Abstract

It is shown that there are relations between the Connes invariant for local v. Neumann algebras belonging to different curved space-times provided these local algebras are connected by a certain asymptotic condition. This asymptotic condition is implied by a scaling limit condition as well as by a condition of connectedness by large translations.