Hilbert C*-systems for actions of the circle group

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.