Categorial Local Quantum Physics

Abstract

Categorial local quantum field theory was suggested as a new paradigm for quantum field theory by Brunetti, Fredenhagen and Verch in 2003 (Commun Math Phys 237:31–68, [7]). In this paradigm quantum field theory is defined to be a covariant functor from the category of certain spacetimes (with isometric embeddings as morphisms) into the category of \(C^{*}\)-algebras (with injective \(C^{*}\)-algebra homomorphisms as morphisms). Further properties of the functor are stipulated axiomatically on the basis of physical considerations. The present paper suggests an additional axiom on the functor that expresses independence of systems as morphism co-possibility. It is argued that this axiom is very natural because it has a direct physical interpretation. The relation of the axiom system containing the morphism co-possibility axiom to other axiom systems is investigated. It will be seen that this axiom system is strictly stronger than the axiom system originally formulated in Brunetti, Fredenhagen, Verch (Commun Math Phys 237:31–68, 2003, [7]), and it is conjectured that it is strictly weaker than the ones formulated in subsequent development of categorial quantum field theory in which the functor is required to be extensible to a tensor functor. Determining the precise status of the axiom system based on morphism co-possibility as independence needs further analysis.