The Poincar\'e Gauge Theory of Gravty and the Immirzi parameter

TL;DR

This paper explores the Poincaré gauge theory of gravity with the Holst term, demonstrating that the Immirzi parameter can be classically measured when fermions are coupled correctly.

Contribution

It introduces a modified minimal coupling procedure for fermions in Poincaré gauge gravity and shows the Immirzi parameter's classical measurability.

Findings

Corrected coupling method for fermions in Poincaré gauge gravity.

Inclusion of Holst term makes the Immirzi parameter classically measurable.

Agreement with Perez and Rovelli's results.

Abstract

The minimal coupling method proved to yield definite and correct physical predictions when applied to fundamental fermions within the framework of Yang--Mills theories of Standard Model. Similarly, the possibility of formulating gravity as the Poincar\'e gauge theory gives the opportunity to produce definite predictions for fermions in the presence of gravitational field. The minimal coupling procedure, however, cannot be applied naively but rather needs to be modified slightly such that it is unambiguous. Application of the corrected coupling method to fermions, together with the inclusion of the Holst term in the gravitational part of the action, leads to the conclusion that the Immirzi parameter is in principle classically measurable, in agreement with the result of Perez and Rovelli.