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Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics. (English) Zbl 0734.46042

Utilizing earlier obtained results [Invent. Math. 98, No.1, 157-218 (1989; Zbl 0691.22002); Ann. Math., II. Ser. 130, No.1, 75-119 (1989; Zbl 0702.46044)] the authors solve a long standing problem by showing that the superselection structure of local quantum theory is determined in terms of a compact group of gauge automorphisms of a field net with normal Bose and Fermi commutation rules. We quote most enlightening authors’ abstract:

“Given the local observables in the vacuum sector fulfilling a few basic principles of local quantum theory, we show that the superselection structure intrinsically determined a priori, can always be described by a unique compact global gauge group acting on a field algebra generated by field operators which commute or anticommute at spacelike separations. The field algebra and the gauge group are constructed simultaneously from the local observables. There will be sectors obeying parastatistics, an intrinsic notion derived from the observables, if and only if the gauge group is non-Abelian. Topological charges would manifest themselves in field operators associated with spacelike cones but not localizable in bounded regions of Minkowski space. No assumptions on the particle spectrum or even on the covariance of the theory is made.However the notion of superselection sector is tailored to theories without massless particles. When translation or Poincaré covariance of the vacuum sector is assumed, our construction leads to a covariant field algebra describing all covariant sectors.”

46L60Applications of selfadjoint operator algebras to physics
81T05Axiomatic quantum field theory; operator algebras
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