Relative Haag Duality for the Free Field in Fock Representation

Details Relative Haag Duality for the Free Field in Fock Representation Relative Haag Duality for the Free Field in Fock Representation

2006-07-25

arxiv.org/abs/math-ph/0607057v1

AnnalesHenriPoincare8:1433-1459,2007

Physics

Mathematical Physics

22 pages

Scientific paper

10.1007/s00023-007-0341-9

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>1 in the vacuum representation. Such property is interesting in view of a theory of superselection sectors for the electromagnetic field.

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