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Classification of subsystems for graded-local nets with trivial superselection structure. (English) Zbl 1087.81039

In the algebraic approach to Quantum Field Theory one starts from a net \({\mathcal A}\) of local observables satisfying the Haag-Kastler axioms including Poincaré covariance and Haag duality. The Doplicher-Roberts construction then yields an associated net \({\mathcal F}\) of field variables revealing the superselection structure and the gauge symmetry of the system. In a previous paper [Commun. Math. Phys. 217, 89–106 (2001; Zbl 0986.81067)], the authors provided a complete classification of subsystems \({\mathcal B}\subset{\mathcal F}\) provided \({\mathcal F}\) has a trivial superselection structure in the sense that any DHR representation is a multiple of the vacuum representation.
The main objective of the present paper is to generalize these classification results to graded local nets. In essence, their aim is to remove the former condition that there be no Fermi-type DHR sectors. Moreover, the authors classify the covariant local extensions of \({\mathcal A}\) which preserve the dynamics.

MSC:

81T05 Axiomatic quantum field theory; operator algebras
81R15 Operator algebra methods applied to problems in quantum theory
46L60 Applications of selfadjoint operator algebras to physics

Citations:

Zbl 0986.81067
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References:

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