Immirzi parameter in quantum general relativity

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