Hilbert C*-systems for actions of the circle group

Hellmut Baumgärtel, Alan L. Carey
October 10, 2000
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: ${\mathcal H}$ is the reference Hilbert space, $\Gamma$ the conjugation and $P$ a basis projection on ${\mathcal H}.$ The group $C(\text{spec} {\mathcal Z}\rightarrow T)$ of $T$-valued functions on $\text{spec} {\mathcal Z}$ turns out to be isomorphic to the stabilizer of ${\mathcal A}$. In particular, examples are presented where the center ${\mathcal Z}$ of the fixed point algebra ${\mathcal A}$ can be calculated explicitly.
open access link doi:10.1016/S0034-4877(01)80048-3
@article{Baumgaertel:2001dy, author = "Baumgaertel, H. and Carey, Alan L.", title = "{Hilbert C*-systems for actions of the circle group}", journal = "Rept. Math. Phys.", volume = "47", year = "2001", pages = "349-361", doi = "10.1016/S0034-4877(01)80048-3", eprint = "math-ph/0010011", archivePrefix = "arXiv", primaryClass = "math-ph", reportNumber = "ESI-2000-940", SLACcitation = "%%CITATION = MATH-PH/0010011;%%" }