Year: 2010
Type: article
Abstract: We relate three-dimensional loop quantum gravity to the combinatorial quantization formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant.We compare the construction of the kinematical Hilbert space and the implementation of the constraints.This leads to an explicit and very interesting relation between the associated operators in the two approaches and sheds light on their physical interpretation.We demonstrate that the quantum group symmetries arising in the combinatorial formalism, the quantum double of the three-dimensional Lorentz and rotation group are also present in the loop formalism.We derive explicit expressions for the action of these quantum groups on the space of cylindrical functions associated with graphs.This establishes a direct
Authors: Catherine Meusburger, Karim Noui
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Award: G4210715029
OpenAlex ID: W2139401611