Extent of the Immirzi Ambiguity in Quantum General Relativity

Details Extent of the Immirzi Ambiguity in Quantum General Relativity Extent of the Immirzi Ambiguity in Quantum General Relativity

2002-03-07

arxiv.org/abs/gr-qc/0203027v1

Class.Quant.Grav.19:L63-2050,2002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, accepted for publication in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/19/8/104

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.

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