Scaling algebras for charged fields and short-distance analysis for localizable and topological charges

TL;DR

This paper extends the scaling algebras method to analyze short-distance behavior of quantum fields with superselection charges, exploring conditions for charge preservation and implications for local and global intertwiners.

Contribution

It introduces a criterion for superselection charge preservation in the scaling limit and studies its consequences for localizable and topological charges.

Findings

Superselection charges can be preserved in the scaling limit under certain conditions.

Preservation of charges implies conjugate charges are also preserved.

For DHR-type charges, all charges' preservation leads to equivalence of local and global intertwiners.

Abstract

The method of scaling algebras, which has been introduced earlier as a means for analyzing the short-distance behaviour of quantum field theories in the setting of the model-independent, operator-algebraic approach, is extended to the case of fields carrying superselection charges. In doing so, consideration will be given to strictly localizable charges ("DHR-type" superselection charges) as well as to charges which can only be localized in regions extending to spacelike infinity ("BF-type" superselection charges). A criterion for the preservance of superselection charges in the short-distance scaling limit is proposed. Consequences of this preservance of superselection charges are studied. The conjugate charge of a preserved charge is also preserved, and for charges of DHR-type, the preservance of all charges of a quantum field theory in the scaling limit leads to equivalence of local and global intertwiners between superselection sectors.