Projective loop quantum gravity. II. Searching for semi-classical states

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Lanery S, Thiemann T
Zeitschrift: Journal of Mathematical Physics
Verlag: AMER INST PHYSICS
Jahr der Veröffentlichung: 2017
Band: 58
Heftnummer: 5
ISSN: 0022-2488


Abstract


In the first paper of this series, an extension of the Ashtekar-Lewandowski state space of loop quantum gravity was set up with the help of a projective formalism introduced by Kijowski. The motivation for this work was to achieve a more balanced treatment of the position and momentum variables (also known as holonomies and fluxes). While this is the first step toward the construction of states semi-classical with respect to a full set of observables, one uncovers a deeper issue, which we analyse in the present article in the case of real-valued holonomies. Specifically, we show that, in this case, there does not exist any state on the holonomy-flux algebra in which the variances of the holonomy and flux observables would all be finite, let alone small. It is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space, for it arises from the structure of the algebra itself. Away out would be to suitably restrict the algebra of observables: we take the first step in this direction in a companion paper. Published by AIP Publishing.



FAU-Autoren / FAU-Herausgeber

Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik


Zitierweisen

APA:
Lanery, S., & Thiemann, T. (2017). Projective loop quantum gravity. II. Searching for semi-classical states. Journal of Mathematical Physics, 58(5). https://dx.doi.org/10.1063/1.4983133

MLA:
Lanery, Suzanne, and Thomas Thiemann. "Projective loop quantum gravity. II. Searching for semi-classical states." Journal of Mathematical Physics 58.5 (2017).

BibTeX: 

Zuletzt aktualisiert 2018-11-08 um 02:16