Representations of nets of $C^*$-algebras over $S^1$

Giuseppe Ruzzi, Ezio Vasselli
April 18, 2011
In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account of the effects of the fundamental group of the spacetime. Using this notion of representation, we prove that any net of C*-algebras over $S^1$ admits faithful representations, and when the net is covariant under Diff$(S^1)$, it admits representations covariant under any amenable subgroup of Diff$(S^1)$.
open access link doi:10.1007/s00220-012-1579-8
@article{Ruzzi:2011an, author = "Ruzzi, Giuseppe and Vasselli, Ezio", title = "{Representations of nets of C*-algebras over S^1}", journal = "Commun. Math. Phys.", volume = "316", year = "2012", pages = "127-149", doi = "10.1007/s00220-012-1579-8", eprint = "1104.3527", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1104.3527;%%" }

Keywords: 
Superselection Theory, conformal qft