The Immirzi parameter in quantum general relativity

Details The Immirzi parameter in quantum general relativity The Immirzi parameter in quantum general relativity

1997-05-22

arxiv.org/abs/gr-qc/9705059v1

Phys.Rev. D57 (1998) 1009-1014

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, no figures, LaTeX, revtex

Scientific paper

10.1103/PhysRevD.57.1009

Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation $U(\iota)$ 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 $U(\iota)$ 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.

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