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Immirzi parameter in quantum general relativity

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 15 Jan 1998Embargo end date: 01 Jan 1997 English Publisher:American Physical Society (APS)Journal:Physical Review D, volume 57, pages 1,009-1,014 (issn: 0556-2821, eissn: 1089-4918,

Authors: Thomas Thiemann; Carlo Rovelli; Carlo Rovelli;

doi: 10.1103/physrevd.57.1009 , 10.48550/arxiv.gr-qc/9705059

arXiv: http://arxiv.org/abs/gr-qc/9705059

Immirzi parameter in quantum general relativity

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Abstract

Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation $U(��)$ on the phase space of general relativity. Immirzi has noticed that in loop quantum gravity this transformation alters the spectra of geometrical quantities. We show that $U(��)$ is a canonical transformation that cannot be implement unitarily in the quantum theory. This implies that there exists a one-parameter quantization ambiguity in quantum gravity, namely a free parameter that enters the construction of the quantum theory. The purpose of this letter is to elucidate the origin and the role of this free parameter.

6 pages, no figures, LaTeX, revtex

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Keywords

FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology

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