Classification of subsystems for graded-local nets with trivial superselection structure

We classify Haag-dual Poincar'e covariant subsystems B subset F of a graded-local net F on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical field net F_A of a net A of local observables satisfying natural assumptions. As a consequence, provided that it has no nontrivial internal symmetries, such an observable net A is generated by (the abstract versions of) the local energy-momentum tensor density and the observable local gauge currents which appear in the algebraic formulation of the quantum Noether theorem. Moreover, for a net A of local observables as above, we also classify the Poincar'e covariant local extensions B supset A which preserve the dynamics.