TRANSITIVITY OF LOCALITY AND DUALITY IN QUANTUM FIELD THEORY

Abstract

Duality conditions for Wightman fields are formulated in terms of the Tomita conjugations S associated with algebras of unbounded operators. It is shown that two fields which are relatively local to an irreducible field fulfilling a condition of this type are relatively local to each other. Moreover, a local net of von Neumann algebras associated with such a field satisfies (essential) duality. These results do not rely on Lorentz covariance but follow from the observation that two algebras of (un)bounded operators with the same Tomita conjugation have the same (un)bounded weak commutant if one algebra is contained in the other.