A Jordan GNS Construction for the Holonomy-Flux *-algebra
| dc.creator | Rios, Michael | |
| dc.date | 2005-05-09 | |
| dc.date | 2005-05-09 | |
| dc.date.accessioned | 2026-07-07T03:29:42Z | |
| dc.date.available | 2026-07-07T03:29:42Z | |
| dc.description | The holonomy-flux *-algebra was recently proposed as an algebra of basic kinematical observables for loop quantum gravity. We show the conventional GNS construction breaks down when the the holonomy-flux *-algebra is allowed to be a Jordan algebra of observables. To remedy this, we give a Jordan GNS construction for the holonomy-flux *-algebra that is based on trace. This is accomplished by assuming the holonomy-flux *-algebra is an algebra of observables that is also a Banach algebra, hence a JB algebra. We show the Jordan GNS construction produces a state that is invariant under all inner derivations of the holonomy-flux *-algebra. Implications for the corresponding Jordan-Schrodinger equation are also discussed. | |
| dc.description | 6 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0505038 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0505038 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/35279 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | A Jordan GNS Construction for the Holonomy-Flux *-algebra | |
| dc.type | text |