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

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;%%"
}

Keywords:

*none*