Hilbert C*-systems for actions of the circle group

Details Hilbert C*-systems for actions of the circle group Hilbert C*-systems for actions of the circle group

2000-10-10

arxiv.org/abs/math-ph/0010011v1

Physics

Mathematical Physics

14 pages, Latex

Scientific paper

10.1016/S0034-4877(01)80048-3

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.

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