Some results concerning the representation theory of the algebra underlying loop quantum gravity

Journal article
(Original article)


Publication Details

Author(s): Sahlmann H
Journal: Journal of Mathematical Physics
Publisher: American Institute of Physics (AIP)
Publication year: 2011
Volume: 52
Journal issue: 1
ISSN: 0022-2488


Abstract


Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of (kinematical) observables and of a representation of A on a measure space over the space of generalized connections. This representation is singled out by its elegance and diffeomorphism covariance. Recently, in the context of the quest for semiclassical states, states of the theory in which the quantum gravitational field is close to some classical geometry, it was realized that it might also be worthwhile to study different representations of the algebra A. The content of the present work is the observation that under some mild assumptions, the mathematical structure of representations of A can be analyzed rather effortlessly, to a certain extent: each representation can be labeled by sets of functions and measures on the space of (generalized) connections that fulfill certain conditions. © 2011 American Institute of Physics.



FAU Authors / FAU Editors

Sahlmann, Hanno Prof. Dr.
Professur für Theoretische Physik


How to cite

APA:
Sahlmann, H. (2011). Some results concerning the representation theory of the algebra underlying loop quantum gravity. Journal of Mathematical Physics, 52(1). https://dx.doi.org/10.1063/1.3525705

MLA:
Sahlmann, Hanno. "Some results concerning the representation theory of the algebra underlying loop quantum gravity." Journal of Mathematical Physics 52.1 (2011).

BibTeX: 

Last updated on 2018-19-04 at 03:19