When do measures on the space of connections support the triad operators of 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
Language: English


Abstract


In this work we investigate the question under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of "no-go theorems" asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces. The flux-observables we consider, play an important role in loop quantum gravity since they can be defined without recurse to a background geometry and they might also be of interest in the general context of quantization of non-Abelian gauge theories. © 2011 American Institute of Physics.



FAU Authors / FAU Editors

Sahlmann, Hanno Prof. Dr.
Professur für Theoretische Physik


How to cite

APA:
Sahlmann, H. (2011). When do measures on the space of connections support the triad operators of loop quantum gravity? Journal of Mathematical Physics, 52(1). https://dx.doi.org/10.1063/1.3525706

MLA:
Sahlmann, Hanno. "When do measures on the space of connections support the triad operators of loop quantum gravity?" Journal of Mathematical Physics 52.1 (2011).

BibTeX: 

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