Extent of the Immirzi Ambiguity in Quantum General Relativity
arXiv:gr-qc/0203027 · doi:10.1088/0264-9381/19/8/104
Abstract
The Ashtekar-Barbero formulation of general relativity admits a one-parameter family of canonical transformations that preserves the expressions of the Gauss and diffeomorphism constraints. The loop quantization of the connection formalism based on each of these canonical sets leads to different predictions. This phenomenon is called the Immirzi ambiguity. It has been recently argued that this ambiguity could be generalized to the extent of a spatially dependent function, instead of a parameter. This would ruin the predictability of loop quantum gravity. We prove that such expectations are not realized, so that the Immirzi ambiguity introduces exclusively a freedom in the choice of a real number.
7 pages, accepted for publication in Classical and Quantum Gravity
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- Near-Horizon Radiation and Self-Dual Loop Quantum Gravity
- Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
- Towards self dual Loop Quantum Gravity
- Shape Dynamical Loop Gravity from a Conformal Immirzi Parameter
- Immirzi Ambiguity, Boosts and Conformal Frames for Black Holes
- Immirzi Ambiguity in the Kinematics of Quantum General Relativity