Quantization of Lorentzian 3D gravity by partial gauge fixing
RMS Barbosa, CP Constantinidis… - … and quantum gravity, 2012 - iopscience.iop.org
RMS Barbosa, CP Constantinidis, Z Oporto, O Piguet
Classical and quantum gravity, 2012•iopscience.iop.orgAbstract D= 2+ 1 gravity with a cosmological constant Λ has been shown by Bonzom and
Livine to present a Barbero–Immirzi-like ambiguity depending on a parameter γ. We make
use of this fact to show that, for Λ> 0, the Lorentzian theory can be partially gauge fixed and
reduced to an SU (2) Chern–Simons theory. We then review the already known quantization
of the latter in the framework of loop quantization for the case of space being topologically a
cylinder. We finally construct, in the same setting, a quantum observable which, although …
Livine to present a Barbero–Immirzi-like ambiguity depending on a parameter γ. We make
use of this fact to show that, for Λ> 0, the Lorentzian theory can be partially gauge fixed and
reduced to an SU (2) Chern–Simons theory. We then review the already known quantization
of the latter in the framework of loop quantization for the case of space being topologically a
cylinder. We finally construct, in the same setting, a quantum observable which, although …
Abstract
D= 2+ 1 gravity with a cosmological constant Λ has been shown by Bonzom and Livine to present a Barbero–Immirzi-like ambiguity depending on a parameter γ. We make use of this fact to show that, for Λ> 0, the Lorentzian theory can be partially gauge fixed and reduced to an SU (2) Chern–Simons theory. We then review the already known quantization of the latter in the framework of loop quantization for the case of space being topologically a cylinder. We finally construct, in the same setting, a quantum observable which, although non-trivial at the quantum level, corresponds to a null classical quantity.
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