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On charged fields with group symmetry and degeneracies of Verlinde’s matrix \(S\). (English) Zbl 0938.81018

Within the framework of algebraic quantum field theory, provided the dimension of spacetime is larger than two, a much celebrated result has been obtained long time ago, namely that the superselection structure (the sectors of states) of the net of local observables is given in terms of representations of some compact group. Starting from the observables, Doplicher and Roberts also showed how to construct an affiliated field net and its set of localized representations. Müger adds to it a negative result. In his article he proves that the field net does not admit nontrivial Doplicher-Haag-Roberts sectors. Unfortunately, the proof presented here relies on the extremely restrictive, perhaps unrealistic assumption that there are only finitely many sectors. It is suggested though that the field net may have nontrivial representations under the weaker Buchholz-Fredenhagen locality assumption.

MSC:

81T05 Axiomatic quantum field theory; operator algebras
46N50 Applications of functional analysis in quantum physics
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