Superselection Sectors and General Covariance.I

TL;DR

This paper investigates charged superselection sectors in locally covariant quantum field theories, establishing a covariant framework linking spacetime embeddings to gauge groups and sectors, and exploring the relation between local and global charges.

Contribution

It introduces a covariant description of superselection sectors using net-cohomology, associating gauge groups to spacetimes and analyzing the covariance of sectors under embeddings.

Findings

Each 4D globally hyperbolic spacetime has a unique symmetric tensor category of sectors.

Embedding between spacetimes induces a group morphism between gauge groups.

The paper conjectures local and global sectors coincide on simply connected spacetimes.

Abstract

This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analize sharply localizable charges, and use net-cohomology of J.E. Roberts as a main tool. We show that to any 4-dimensional globally hyperbolic spacetime it is attached a unique, up to equivalence, symmetric tensor $\Crm^*-$category with conjugates (in case of finite statistics); to any embedding between different spacetimes, the corresponding categories can be embedded, contravariantly, in such a way that all the charged quantum numbers of sectors are preserved. This entails that to any spacetime is associated a unique gauge group, up to isomorphisms, and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups. This form of covariance between sectors also brings to light the issue whether local and global sectors are the same. We conjecture this holds that at least on simply connected spacetimes. It is argued that the possible failure might be related to the presence of topological charges. Our analysis seems to describe theories which have a well defined short-distance asymptotic behaviour.