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

We classify Haag-dual Poincaré 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 Poincaré covariant local extensions $\B \supset \A$ which preserve the dynamics.

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