A Jordan GNS Construction for the Holonomy-Flux *-algebra
General Relativity and Quantum Cosmology
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.gr-qc/0505038,
title = {A Jordan GNS Construction for the Holonomy-Flux *-algebra},
author = {Michael Rios},
journal= {arXiv preprint arXiv:gr-qc/0505038},
year = {2007}
}
Comments
6 pages, no figures