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Journal Article

#### When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?

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##### Fulltext (public)

gr-qc_0207112

(Preprint), 223KB

JMP52_012503.pdf

(Any fulltext), 868KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Sahlmann, H. (2011). When Do Measures on the Space of Connections Support the Triad
Operators of Loop Quantum Gravity?* Journal of Mathematical Physics,* *52*:
012503. doi:10.1063/1.3525706.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-112F-1

##### 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 recourse to a background geometry,
and they might also be of interest in the general context of quantization of
non-Abelian gauge theories.