Immirzi parameter and fermions with non-minimal coupling

TL;DR

This paper demonstrates that the Immirzi parameter does not influence the classical effective action in gravity coupled to fermions, even with non-minimal coupling, indicating it is not observable in classical physics.

Contribution

The study shows that, despite explicit torsion dependence, the Immirzi parameter does not affect the classical effective action in fermion-coupled gravity.

Findings

Effective action is independent of the Immirzi parameter

Torsion depends explicitly on the Immirzi parameter

Immirzi parameter is not detectable in classical theory

Abstract

We clarify the role played by the Immirzi parameter in classical gravity coupled to fermions. Considering the general non-minimal coupling, we show that, although the torsion depends explicitly on the Immirzi parameter, in a suitable parametrization the effective action obtained by integrating out the spin-connection is independent of it. Thus the Immirzi parameter is not detectable in classical theory even after coupling of fermions.