Extent of the Immirzi Ambiguity in Quantum General Relativity

TL;DR

This paper investigates the Immirzi ambiguity in loop quantum gravity, demonstrating that it is limited to a real parameter and cannot be extended to a spatially dependent function, thus preserving some predictability.

Contribution

The paper proves that the Immirzi ambiguity remains a single real parameter and cannot be generalized to a spatially dependent function, countering recent claims.

Findings

The Immirzi ambiguity is limited to a real parameter.

It cannot be extended to a spatially dependent function.

This preserves some predictability in loop quantum gravity.

Abstract

The Ashtekar-Barbero formulation of general relativity admits a one-parameter family of canonical transformations that preserves the expressions of the Gauss and diffeomorphism constraints. The loop quantization of the connection formalism based on each of these canonical sets leads to different predictions. This phenomenon is called the Immirzi ambiguity. It has been recently argued that this ambiguity could be generalized to the extent of a spatially dependent function, instead of a parameter. This would ruin the predictability of loop quantum gravity. We prove that such expectations are not realized, so that the Immirzi ambiguity introduces exclusively a freedom in the choice of a real number.