- 93-241 H.J. Borchers, Jakob Yngvason
- Transitivity of Locality and Duality in Quantum Field Theory.
Some Modular Aspects
(74K, plain TeX)
Oct 8, 93
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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 that 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.