Bogoliubov transformations and localized morphisms for free Dirac fields

The construction of localized morphisms of the algebra of quasilocal observables in free Dirac theory via Bogolyubov transformations is investigated. If the observables are selected from the fields by invariance under the abelian gauge group U(1) suitably chosen multiplication operators in one-particle position space induce nontrivial localized automorphisms in two, but not in four spacetime dimensions. In case of non-abelian gauge groups non-surjective Bogolyubov transformations have to be considered. A criterion for implementability of such a transformation ρ in a Fock state ω is given. Provided that ω omikron ρ is again a Fock state explicit expressions for the implementing isometries are obtained, but, unfortunately, transformations of this type do not lead to localized morphisms in the sense of Doplicher, Haag and Roberts. (orig.)