Classification of Subsystems for Local Nets with Trivial Superselection Structure

Details Classification of Subsystems for Local Nets with Trivial Superselection Structure Classification of Subsystems for Local Nets with Trivial Superselection Structure

2000-02-24

arxiv.org/abs/math/0002204v1

Commun.Math.Phys. 217 (2001) 89-106

Mathematics

Operator Algebras

31 pages, LaTex

Scientific paper

10.1007/PL00005550

Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is the fixed point net under a compact group action on one component in a suitable tensor product decomposition of F. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors.

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