Comment on “Immirzi parameter in quantum general relativity”

The Immirzi parameter is a free parameter which appears in the physical predictions of loop quantum gravity and is sometimes viewed as a quantization ambiguity. Interpretations have been offered for the Immirzi ambiguity, but there does not appear to be a clear understanding or even a consensus about its origin and significance. We show that a previously discussed example containing a “finite dimensional analogue” of the Immirzi ambiguity is fallacious, in the sense that the ambiguity in this example is not intrinsic to the system, but introduced artificially by compactifying the configuration space.