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@article{faucris.320043309,
abstract = {We consider the quantization of gravity as an S L ( 2 , C ) gauge theory in terms of Ashtekarâ€™s selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII). We start from a holomorphic phase space formulation. It is then natural to push for a quantization in terms of holomorphic wave functions. Thus we consider holomorphic cylindrical wave functions over S L ( 2 , C ) connections. We use an overall phase ambiguity of the complex selfdual action to obtain Poisson brackets that mirror those of the real theory. We then show that there is a representation of the corresponding canonical commutation relations in the space of holomorphic cylindrical functions. We describe a class of cylindrically consistent measures that implements RCI. We show that spin networks with S U ( 2 ) intertwiners form a basis for gauge invariant states. They are still mutually orthogonal, but the normalisation is different than for the Ashtekar-Lewandowski measure for S U ( 2 ) . We do not consider RCII in the present article. Work on RCII is ongoing and will be presented elsewhere.},
author = {Sahlmann, Hanno and Seeger, Robert},
doi = {10.1088/1361-6382/ad2ceb},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {Ashtekar variables; loop quantum gravity; measures on spaces of connections; selfdual variables},
note = {CRIS-Team Scopus Importer:2024-03-22},
peerreviewed = {Yes},
title = {{Revisiting} loop quantum gravity with selfdual variables: {Hilbert} space and first reality condition},
volume = {41},
year = {2024}
}