Abstract
Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation 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 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.
- Received 14 May 1997
DOI:https://doi.org/10.1103/PhysRevD.57.1009
©1998 American Physical Society