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Communications in Mathematical Physics

, Volume 86, Issue 1, pp 111–141 | Cite as

Normal product states for fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa2 quantum field model

  • Stephen J. Summers
Article

Abstract

We present sufficient conditions that imply duality for the algebras of local observables in all Abelian sectors of all locally normal, irreducible representations of a field algebra if twisted duality obtains in one of these representations. It is verified that the Yukawa2 model satisfies these conditions, yielding the first proof of duality for the observable algebra in all coherent charge sectors in this model. This paper also constitutes the first verification of the assumptions of the axiomatic study of the structure of superselection sectors by Doplicher, Haag and Roberts in an interacting model with nontrivial sectors. The existence of normal product states for the free Fermi field algebra and, thus, the verification of the “funnel property” for the associated net of local algebras are demonstrated.

Keywords

Irreducible Representation Quantum Computing Field Model Free Fermi Local Observable 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Stephen J. Summers
    • 1
  1. 1.Fachbereich 4Universität OsnabrückOsnabrückGermany

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