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No abstract

We isolate an abstract algebraic property which implies duality in all locally normal, irreducible representations of a quasilocal C*-algebra if it holds together with two more specific conditions. All these conditions holding for the CCR-algebra in d ^ 2 space time dimensions duality follows for representations of the two-dimensional CCR-algebra generated by pure Wightman states of P(Φ) 2 -theories. We then show that algebras of this kind have no nontrivial locally generated superselection sectors which for d ^ 3 yields a first approximation to a quantum analogue of Derrick's theorem.

We give a simple sufficient condition for a von Neumann algebra to be Type III and apply it to some classes of algebras in QFT. For dilatation invariant local systems in particular we find that all sufficiently regular local algebras are Type III.