Relative Haag Duality for the Free Field in Fock Representation

We consider a natural generalization of Haag duality to the case in which the observable algebra is restricted to a subset of the space-time and is not irreducible: the commutant and the causal complement have to be considered relatively to the ambient space. We prove this relative form of Haag duality under quite general conditions for the free scalar and electromagnetic field of space dimension d ≥ 2 in the vacuum representation. Such property is interesting in view of a theory of superselection sectors for the electromagnetic field. Supported by the EU network “Quantum Spaces – Noncommutative Geometry” HPRN-CT-2002-00280. Submitted: August 1, 2006. Accepted: March 2, 2007.