Physical effects of the Immirzi parameter

TL;DR

The paper demonstrates that the Immirzi parameter influences classical physics by affecting fermion interactions, challenging the belief that it only has quantum significance and showing it can have observable effects.

Contribution

It reveals that the Immirzi parameter impacts equations of motion in the presence of fermions, leading to observable four-fermion interactions.

Findings

Immirzi parameter affects fermion coupling

It appears in equations of motion with fermions

Observable four-fermion interactions depend on the Immirzi parameter

Abstract

The Immirzi parameter is a constant appearing in the general relativity action used as a starting point for the loop quantization of gravity. The parameter is commonly believed not to show up in the equations of motion, because it appears in front of a term in the action that vanishes on shell. We show that in the presence of fermions, instead, the Immirzi term in the action does not vanish on shell, and the Immirzi parameter does appear in the equations of motion. It determines the coupling constant of a four-fermion interaction. Therefore the Immirzi parameter leads to effects that are observable in principle, even independently from nonperturbative quantum gravity.