The paper contains constructions of Hilbert systems for the action of the circle group $T$ using subgroups of implementable Bogoljubov unitaries w.r.t. Fock representations of the Fermion algebra for suitable data of the selfdual framework: ${ \cal H}$ is the reference Hilbert space, $\Gamma$ the conjugation and $P$ a basis projection on ${ \cal H}.$ The group $C({ spec} { \cal Z}\to T)$ of $T$-valued functions on ${ spec} { \cal Z}$ turns out to be isomorphic to the stabilizer of ${ \cal A}$. In particular, examples are presented where the center ${ \cal Z}$ of the fixed point algebra ${ \cal A}$ can be calculated explicitly.
Categories: math-ph math.MP
