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

Claudio D'Antoni, Gerardo Morsella, and Rainer Verch

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Submission date: 03. Mar. 2004
published in: Annales Henri Poincaré, 5 (2004) 5, p. 809-870 
DOI number (of the published article): 10.1007/s00023-004-0183-7
Bibtex
MSC-Numbers: 81T05
Keywords and phrases: renormalization group, algebraic quantum field theory, charge confinement

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, opertor-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 lead to equivalence of local and global intertwiners between superselection sectors.