Journal article
(Original article)


When do measures on the space of connections support the triad operators of loop quantum gravity?


Publication Details
Author(s): Sahlmann H
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.



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).

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