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

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-112F-1 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-1130-C
Genre: Journal Article

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 Creators:
Sahlmann, Hanno1, Author
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1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 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.

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 Dates: 2002-07-292011-01-202011
 Publication Status: Published in print
 Pages: LaTeX, 21 pages, 5 figures; v3: some typos and formulations corrected, some clarifications added, bibliography updated; article is now identical to published version
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 Rev. Method: -
 Identifiers: arXiv: gr-qc/0207112
DOI: 10.1063/1.3525706
URI: http://arxiv.org/abs/gr-qc/0207112
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Title: Journal of Mathematical Physics
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. [etc.] : American Institute of Physics
Pages: - Volume / Issue: 52 Sequence Number: 012503 Start / End Page: - Identifier: ISSN: 0022-2488
CoNE: /journals/resource/954922836227