Phys. Rev. D 57, 1009–1014 (1998)

Immirzi parameter in quantum general relativity

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Carlo Rovelli^*
Physics Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Center for Gravity and Geometry, Penn State University, University Park, Pennsylvania 16802

Thomas Thiemann^†
Physics Department, Harvard University, Cambridge, Massachusetts 02118

Received 14 May 1997; published in the issue dated 15 January 1998

Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation U(γ) 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(γ) is a canonical transformation that cannot be implemented unitarily in 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 paper is to elucidate the origin and the role of this free parameter.

URL:

http://link.aps.org/doi/10.1103/PhysRevD.57.1009

DOI:

10.1103/PhysRevD.57.1009

PACS:

04.60.Ds

^*Email address: rovelli@pitt.edu

^†Email address: thiemann@math.harvard.edu

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Phys. Rev. D 57, 1009–1014 (1998)

Immirzi parameter in quantum general relativity

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