Nieh-Yan Invariant and Fermions in Ashtekar-Barbero-Immirzi Formalism

In order to introduce an interaction between gravity and fermions in the Ashtekar-Barbero-Immirzi formalism without affecting classical dynamics a non-minimal term is necessary. The non-minimal term together with the Holst modification to the Hilbert-Palatini action reconstruct the Nieh-Yan invariant. As a consequence the Immirzi parameter, differently from the minimal coupling approach, does not affect the classical dynamics, which is described by the Einstein-Cartan action.