Classification of Subsystems for Local Nets¶with Trivial Superselection Structure

Abstract:

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 of the form ℱ₁ ^G⊗I for a suitable decomposition ℱ=ℱ₁⊗ℱ₂ and a compact group action. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors.