Asymptotic morphisms and superselection theory in the scaling limit (Q470338)

Conti and Morsella use the algebraic approach to quantum field theory of Doplicher, Haag and Roberts where one assumes the existence of a local net of operator algebras satisfying physical axioms. Another powerful mathematical tool is provided by Noncommutative Geometry as developed by Connes. In the present paper, Conto and Morsella introduce a variant of the concept of asymptotic morphism of Connes and Higson. They show that this concept describes the superselection structure of the short distance scaling limit states in the context of a local net. Interesting connections between Quantum Field Theory in general and the language of Noncommutative Geometry have been detected and investigated by a number of authors. But the main motivation for the present paper was a question posed by Doplicher. He asks whether it is possible to describe all superselection sectors of the scaling limit nets, introduced by Buchholz and Verch, using objects related to the Connes-Higson asymptotic morphism. It turns out that this can be done with certain restrictions. The paper ends with an outlook on open questions, interesting issues and future directions.