Independence Conditions for Nets of Local Algebras as Sheaf Conditions

Sander A. M. Wolters, Hans Halvorson

Published 2013-09-22, updated 2013-10-17Version 2

We apply constructions from topos-theoretic approaches to quantum theory to algebraic quantum ?eld theory. Thus a net of operator algebras is reformulated as a functor that maps regions of spacetime into a category of ringed topoi. We ask whether this functor is a sheaf, a question which is related to the net satisfying certain kinematical independence conditions. In addition, we consider a C*-algebraic version of Nuiten's recent sheaf condition, and demonstrate how it relates to C*-independence of the underlying net of operator algebras.