Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-06-02
Class. Quant Grav.27:225007, 2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
13 pages, 2 figures. v2: Some clarifications added, typos removed. Virtually identical with published version
Scientific paper
10.1088/0264-9381/27/22/225007
In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and diffeomorphism constraints can be implemented. With the present article, we streamline and extend his treatment. In particular, we show that the standard regularization of the geometric operators leads to well defined operators in the new representations, and we work out their properties fully. We also give details on the implementation of the constraints. All of this is done in such a way as to show that the standard representation is a particular (and in some ways exceptional) case of the more general constructions. This does not mean that these new representations are as fundamental as the standard one. Rather, we believe they might be useful to find some form of effective theory of loop quantum gravity on large scales.
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